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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Submanifolds associated with graphs
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by Alfonso Carriazo and Luis M. Fernández PDF
Proc. Amer. Math. Soc. 132 (2004), 3327-3336 Request permission

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
  • Bang-Yen Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Louvain, 1990. MR 1099374
  • Frank Harary, Graph theory, Addison-Wesley Publishing Co., Reading, Mass.-Menlo Park, Calif.-London 1969. MR 0256911
  • Neculai Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 40 (1994), no. 1, 55–61. MR 1328947
  • Kentaro Yano and Masahiro Kon, Structures on manifolds, Series in Pure Mathematics, vol. 3, World Scientific Publishing Co., Singapore, 1984. MR 794310
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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
  • MR Author ID: 655479
  • 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
  • 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
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 3327-3336
  • MSC (2000): Primary 53C40, 05C90
  • DOI: https://doi.org/10.1090/S0002-9939-04-07473-8
  • MathSciNet review: 2073309