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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Submanifolds associated with graphs


Authors: Alfonso Carriazo and Luis M. Fernández
Journal: Proc. Amer. Math. Soc. 132 (2004), 3327-3336
MSC (2000): Primary 53C40, 05C90
Published electronically: 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.


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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: http://dx.doi.org/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
Published electronically: June 22, 2004
Additional Notes: The authors were partially supported by the PAI project (Junta de Andalucía, Spain, 2002).
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2004 American Mathematical Society