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CR-warped submanifolds in Kaehler manifolds. (English) Zbl 1351.32064

Dragomir, Sorin (ed.) et al., Geometry of Cauchy-Riemann submanifolds. Singapore: Springer (ISBN 978-981-10-0915-0/hbk; 978-981-10-0916-7/ebook). 1-25 (2016).
Summary: 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.
For the entire collection see [Zbl 1350.32001].

MSC:

32V99 CR manifolds
32Q15 Kähler manifolds
53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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