Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Submanifolds associated with graphs

Author(s): Alfonso Carriazo; Luis M. Fernández
Journal: Proc. Amer. Math. Soc. 132 (2004), 3327-3336.
MSC (2000): Primary 53C40, 05C90
Posted: June 22, 2004
MathSciNet review: 2073309
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Abstract: In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.

References:

1.: B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Louvain, 1990. MR 92d:53047
2.: F. Harary, Graph theory, Addison-Wesley, Reading, Mass., 1969. MR 41:1566
3.: N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi. 40 (1994), 55-61. MR 96d:53066
4.: K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics 3, World Scientific, Singapore, 1984. MR 86g:53001

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Additional Information:

Alfonso Carriazo
Affiliation: Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla, Apdo. Correos 1160, 41080-Sevilla, Spain
Email: carriazo@us.es

Luis M. Fernández
Affiliation: Department of Geometry and Topology, Faculty of Mathematics, University of Sevilla, Apdo. Correos 1160, 41080-Sevilla, Spain
Email: lmfer@us.es

DOI: 10.1090/S0002-9939-04-07473-8
PII: S 0002-9939(04)07473-8
Keywords: Almost Hermitian manifold, CR-submanifold, slant submanifold, graph theory
Received by editor(s): July 25, 2001
Posted: June 22, 2004
Additional Notes: The authors were partially supported by the PAI project (Junta de Andaluc{í}a, Spain, 2002).
Communicated by: Mohan Ramachandran
Copyright of article: Copyright 2004, American Mathematical Society

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