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CR-Warped Submanifolds in Kaehler Manifolds

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Geometry of Cauchy-Riemann Submanifolds

Abstract

The warped product \(N_1\times _f N_2\) of two Riemannian manifolds \((N_1,g_1)\) and \((N_2,g_2)\) is the product manifold \(N_1\times N_2\) equipped with the warped product metric \(g=g_1+f^2 g_2\), where f is a positive function on \(N_1\). Warped products play very important roles in differential geometry as well as in physics. A submanifold M of a Kaehler manifold \(\tilde{M}\) is called a CR-warped product if it is a warped product \(M_T\times _f N_\perp \) of a complex submanifold \(M_T\) and a totally real submanifold \(M_\perp \) of \(\tilde{M}\). In this article we survey recent results on warped product and CR-warped product submanifolds in Kaehler manifolds. Several closely related results will also be presented.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI, 48824-1027, USA

    Bang-Yen Chen

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  1. Bang-Yen Chen
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Correspondence to Bang-Yen Chen .

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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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Chen, BY. (2016). CR-Warped Submanifolds in 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_1

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