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INVARIANT SUBMANIFOLDS OF CONTACT (κ, μ)-MANIFOLDS

Published online by Cambridge University Press:  01 September 2008

BENIAMINO CAPPELLETTI MONTANO ,
LUIGIA DI TERLIZZI  and
MUKUT MANI TRIPATHI
BENIAMINO CAPPELLETTI MONTANO
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy e-mail: [email protected]
LUIGIA DI TERLIZZI
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125 Bari, Italy e-mail: [email protected]
MUKUT MANI TRIPATHI
Affiliation:
Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, India
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Abstract

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Invariant submanifolds of contact (κ, μ)-manifolds are studied. Our main result is that any invariant submanifold of a non-Sasakian contact (κ, μ)-manifold is always totally geodesic and, conversely, every totally geodesic submanifold of a non-Sasakian contact (κ, μ)-manifold, μ ≠ 0, such that the characteristic vector field is tangent to the submanifold is invariant. Some consequences of these results are then discussed.

Keywords

Primary 53C40Secondary 53C2553D1053D15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 499 - 507
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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