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CR-Submanifolds and \(\delta \)-Invariants

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Geometry of Cauchy-Riemann Submanifolds

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Abstract

Curvature invariants are the \(N^o\,1\) Riemannian invariants and the most natural ones. Curvatures invariants play key roles in physics as well. Classically, among the Riemannian curvature invariants, people have been studying scalar and Ricci curvatures in great detail. On the other hand, the author introduced in the early 1990s, a new type of curvature invariants on Riemannian manifolds, called \(\delta \)-invariants. The \(\delta \)-curvatures are very different in nature from the “classical” scalar and Ricci curvatures. \(\delta \)-invariants are known to play some important roles in several areas in mathematics. In this article, we survey recent results on CR-submanifolds in complex space forms which are related to \(\delta \)-invariants and Riemannian submersions.

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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-Submanifolds and \(\delta \)-Invariants. 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_2

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