Artículos (Geometría y Topología)
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Artículo Algunas aplicaciones de las curvas de Bertrand(Redalyc, 2007-12-14) González Herrera, Antonio; Núñez Valdés, Juan; Universidad de Sevilla. Departamento de Geometría y TopologíaThis paper deals with Bertrand curves. Some proofs of its main properties simplifying the habitual ones are shown. Some concepts of previous papers by several authors, relating Bertrand curves with other different types of curves and with some surfaces, are also improved.Artículo The space of almost complex 2-spheres in the 6-spheres(American Mathematical Society, 2014-11-24) Fernández Fernández, Luis Manuel; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM327: Geometría (Semi) Riemanniana y AplicacionesThe complex dimension of the space of linearly full almost complex 2-spheres of area 4πd in the round 6-sphere is calculated to be d + 8. Explicit examples of these objects are constructed for every integer value of the degree, d ≥ 6, d = 7. Furthermore, it is shown that when d = 6 this space is isomorphic to the group G2(C), and when d = 7 this space is empty. We also show that the dimension of the space of nonlinearly full almost complex 2-spheres of area 4πd in the round 6-sphere is 2d + 5.Artículo Mathematical tools for the future: Graph Theory and graphicable algebras(Elsevier, 2013-01-23) Núñez Valdés, Juan; Silvero Casanova, Marithania; Villar Liñán, María Trinidad; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM326: Geometria Diferencial y Teoria de LieThis study constitutes the continuation of innovative research in Discrete Mathematics introduced in earlier papers on algebras in general, regarding the use of graphs to study the particular case of graphicable algebras, which form a subset of evolution algebras. Evolution algebras are particularly interesting since they are intrinsically linked with other mathematical fields, such as group theory, stochastics processes, and dynamical systems, for instance. Our advances in this study are obtained by setting a natural correspondence between evolution algebras and direct graphs, in order to translate the general concepts of graphicable algebras: subalgebra, ideal, centralizer, normalizer…to the language of graphs. These translations will enable advances in the application of these algebras to various branches of Mathematics.Artículo A new class of metric f-manifolds(jstor, 2018-06-30) Alegre Rueda, Pablo Sebastián; Fernández Fernández, Luis Manuel; Prieto Martín, Alicia; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM327: Geometria (Semi) Riemanniana y AplicacionesWe introduce a new general class of metric f-manifolds which we call (almost) trans-S-manifolds and includes Smanifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifolds studied previously. We prove their main properties and we present many examples which justify their study.Artículo Simplicial fibrations(Springer, 2021-01-12) Fernández Ternero, Desamparados; García Calcines, José Manuel; Macías Virgós, Enrique; Vilches Alarcón, José Antonio; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM326: Geometria Diferencial y Teoria de LieWe undertake a systematic study of fibrations in the setting of abstract simplicial complexes, where the concept of “homotopy” has been replaced by that of “contiguity”. Then, a fibration will be a simplicial map satisfying the “contiguity lifting property”. This definition turns out to be equivalent to that introduced by Minian, established in terms of a cylinder construction . This allows us to prove several properties of simplicial fibrations which are analogous to the classical ones in the topological setting, for instance: all the fibers of a fibration with connected base have the same strong homotopy type and any fibration with a strongly collapsible base is fibrewise trivial. We also introduce the concept of “simplicial finite-fibration”, that is, a simplicial map which has the contiguity lifting property only for finite complexes. Then, we prove that the path fibration is a finite-fibration, where is the simplicial complex of Moore paths introduced by Grandis. This result allows us to prove that any simplicial map factors through a finite-fibration, up to a P-homotopy equivalence. Moreover, we prove a simplicial version of a Varadarajan result for fibrations, relating the LS-category of the total space, the base and the generic fiber. Finally, we introduce a definition of “Švarc genus” of a simplicial map and we are able to compare the Švarc genus of path fibrations with the notions of simplicial LS-category and simplicial topological complexity introduced by the authors in several previous papers.Artículo The evolution operator of evolution algebras(Taylor & Francis, 2021-01-17) Fernández Ternero, Desamparados; Gómez Sousa, Víctor Manuel; Núñez Valdés, Juan; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM326: Geometria Diferencial y Teoria de LieThis paper deals with the evolution operator of evolution algebras. The main goal is to obtain novel results of this operator, both in the case in which it is a derivation and when it is a homomorphism of algebras. These new results constitute a criterion for classifying evolution algebras satisfying one of these conditions. An algorithm to obtain all these degenerate evolution algebras starting from those of smaller dimensions is also constructed.Artículo Strong Discrete Morse Theory and Simplicial L–S Category: A Discrete Version of the Lusternik–Schnirelmann Theorem(Springer, 2019-07-29) Fernández Ternero, Desamparados; Macías Virgós, Enrique; Scoville, Nicholas A.; Vilches Alarcón, José Antonio; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM326: Geometria Diferencial y Teoria de LieWe prove a discrete version of the Lusternik–Schnirelmann theorem for discrete Morse functions and the recently introduced simplicial Lusternik–Schnirelmann category of a simplicial complex. To accomplish this, a new notion of critical object of a discrete Morse function is presented, which generalizes the usual concept of critical simplex (in the sense of R. Forman). We show that the non-existence of such critical objects guarantees the strong homotopy equivalence (in the Barmak and Minian’s sense) between the corresponding sublevel complexes. Finally, we establish that the number of critical objects of a discrete Morse function defined on K is an upper bound for the non-normalized simplicial Lusternik–Schnirelmann category of K.Artículo A Characterization of Associative Evolution Algebras(Universal Wiser, 2023-02-13) Fernández Ternero, Desamparados; Gómez Sousa, Víctor Manuel; Núñez Valdés, Juan; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM326: Geometria Diferencial y Teoria de LieEvolution algebras are non-associative in general, that is, the binary multiplication law is not associative. However, there exist some of them that are associative. In this paper we deal with these last ones. We give an explicit classification of these algebras and show that the concept of associativity is equivalent to the existence of an unitary element for non-degenerate evolution algebras. We also explicitly describe the derivation space of these algebras.Artículo Generalized Sasakian space forms and conformal changes of metric(Springer, 2011-02-10) Alegre Rueda, Pablo Sebastián; Carriazo Rubio, Alfonso; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM327: Geometria (Semi) Riemanniana y AplicacionesThe study of generalized Sasakian space forms is continued in this paper. The behavior of such spaces under generalized D-conformal deformations is analyzed. As a consequence, new examples of generalized Sasakian space forms are given.Artículo CR-submanifolds of Lorentzian manifolds(DergiPark, 2009-04-30) Alegre Rueda, Pablo Sebastián; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM327: Geometria (Semi) Riemanniana y AplicacionesThis paper is about the talk given in the VIth Geometry Symposium in Bursa, Turkey, on July 2008. We present the notion of CR-submanifolds of a Lorentzian almost contact manifold, study their principal characteristics and the particular cases in which the manifold is Lorentzian Sasakian manifold or a Lorentzian Sasakian space form. We also presnt some new results for CR-submanifolds of a generalized Lorentzian Sasakian space form.Artículo Structures on generalized Sasakian-space-forms(Elsevier, 2008-06-06) Alegre Rueda, Pablo Sebastián; Carriazo Rubio, Alfonso; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM327: Geometria (Semi) Riemanniana y AplicacionesIn this paper, contact metric and trans-Sasakian generalized Sasakian-space-forms are deeply studied. We present some general results for manifolds with dimension greater than or equal to 5, and we also pay a special attention to the 3-dimensional cases.Artículo Generalized Sasakian-space-forms(Springer, 2004-12-01) Alegre Rueda, Pablo Sebastián; Blair, David E.; Carriazo Rubio, Alfonso; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. FQM327: Geometria (Semi) Riemanniana y AplicacionesGeneralized Sasakian-space-forms are introduced and studied. Many examples of these manifolds are presented, by using some different geometric techniques such as Riemannian submersions, warped products or conformal and related transformations. New results on generalized complex-space-forms are also obtained.Artículo Covering-based numbers related to the LS-category of finite spaces(Unión Matemática Argentina, 2024-09-03) Cárdenas Escudero, Manuel Enrique; Flores Díaz, Ramón Jesús; Quintero Toscano, Antonio Rafael; Villar Liñán, María Trinidad; Universidad de Sevilla. Departamento de Geometría y TopologíaIn this paper, Lusternik-Schinrelmann and geometric category of finite spaces are considered. We define new numerical invariants of these spaces derived from the geometric category and present an algorithmic approach for its effective computation. The analysis is undertaken by combining homotopic features of the spaces, algorithms and tools from the theory of graphs and hypergraphs. We also provide a number of examples.Artículo Uncountable graphs with all their vertices in one face(Akademiai Kiado Rt., 2006) Boza Prieto, Luis; Fedriani, E.M.; Nuñez Valdés, Juan; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)Chartrand and Harary characterized finite outer-planar graphs, and Wagner studied uncountable graphs admitting a planar embedding. We continue this research for those outer-S graphs in surfaces S by studying un countable graphs admitting S-embeddings with all their vertices in the same face (namely, outer-S embeddings).Artículo Outerplanarity without accumulation in the cylinder and the Möbius Band(Board, 2013) Boza Prieto, Luis; Fedriani, Eugenio E.; Núñez Valdés, Juan; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)In this paper we explicitly characterize the outer-embeddings without vertex accumulation points in the open cylinder and in the Mo¨bius strip. In the first case, the list of forbidden minors consists of 11 graphs. In the second, we provide the list of 92 forbidden minors as well as the list of 182 forbidden subgraphs.Artículo Outer-embeddability in certain pseudosurfaces arising from three spheres(North Holland (Elsevier), 2010) Boza Prieto, Luis; Fedriani, Eugenio M.; Nuñez Valdés, Juan; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Geometría y TopologíaIn this paper we study graph embeddings in pseudosurfaces formed by three spheres sharing at most two points each pair, and in such a way that all vertices in the graph are in the same face. Our results and examples show that the behaviour of outer embeddings in these pseudosurfaces is rather different from embeddings on the pseudosurfaces considered in the literature so far.Artículo A new method for classifying complex filiform Lie algebras(Elsevier Science, 2001) Boza Prieto, Luis; Fedriani, E.M.; Núñez Valdés, Juan; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)In this paper, we describe a new method to classify complex filiform Lie algebras based on the concept of isomorphism between Lie algebras. This method, which has the advantage of being applied to any dimension, gives the families of algebras in each dimension in an explicit way. In order to apply, only the corresponding structure the- orem of complex filiform Lie algebras in each dimension is needed. As a consequence of our study, we also predict that the increase (in terms of quotiens) in the number of algebras families when passing from even dimension to odd dimension tends to 1 whereas it grows in a no finite way if passing from odd dimension to immediate even dimension.Artículo A Hahn-Mazurkiewicz Theorem for generalized Peano continua(Springer, 1998) Ayala Gómez, Rafael; Chávez de Diego, María José; Quintero Toscano, Antonio Rafael; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)S. Mazurkiewicz remarked after his proof of the celebrated HahnMazurkiewicz Theorem ([5]) that any generalized Peano continuum is the continuous image of the half-line 0; 1 but the converse does not hold. Therefore continuous images of 0; 1 do not characterize generalized Peano continua. In this paper we use perfect maps and trees to obtain an analogue of the Hahn-Mazurkiewicz Theorem for generalized Peano continua in the spirit of the classical Hahn-Mazurkiewicz Theorem.Artículo On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor(Institute of Mathematics, Polish Academy of Sciences, 1998) Ayala Gómez, Rafael; Chávez de Diego, María José; Quintero Toscano, Antonio Rafael; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the 2-sphere. We also give a characterization of the Peano generalized continua which admit closed embeddings in the Euclidean plane.Capítulo de Libro On irreductible triangulations of Punctured Torus and Punctured Klein Bottle(Editorial UCA, 2007) Chávez de Diego, María José; Quintero Toscano, Antonio Rafael; Villar Liñán, María Trinidad; Universidad de Sevilla. Departamento de Geometría y Topología; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)We extend Lawrencenko and Negami’s results in [4, 5] by establishing lower and upper bounds for the number of irreducible triangulations of the punctured torus and the punctured Klein bottle.