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Geometry of Cauchy-Riemann Submanifolds pp 343–359Cite as

CR-Submanifolds of Semi-Riemannian Kaehler Manifolds

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Abstract

First, we review the preliminaries and basic formulas for the CR-submanifold of a Kaehler manifold. Allowing the Kaehler metric to be of all signatures compatible with the Hermitian structure, we recall the results on mixed foliate, normal mixed totally geodesic and totally umbilical CR-submanifolds of a Kaehler manifold. Finally, CR-submanifolds have been studied within the frame-work of space-time (in particular, of general relativity).

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Authors and Affiliations

  1. University of New Haven, West Haven, CT, 06516, USA

    Ramesh Sharma

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  1. Ramesh Sharma
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Correspondence to Ramesh Sharma .

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Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Potenza, Italy

    Sorin Dragomir

  2. Dept. of Maths., Faculty of Natural Sci, Jamia Millia Islamia,, New Delhi, Delhi, India

    Mohammad Hasan Shahid

  3. Department of Mathematics, King Abdul Aziz University, Thuwal, Saudi Arabia

    Falleh R. Al-Solamy

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Sharma, R. (2016). CR-Submanifolds of Semi-Riemannian Kaehler Manifolds. In: Dragomir, S., Shahid, M., Al-Solamy, F. (eds) Geometry of Cauchy-Riemann Submanifolds. Springer, Singapore. https://doi.org/10.1007/978-981-10-0916-7_12

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