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Problems of Extrinsic Geometry of Foliations

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Abstract

This survey is devoted to particular problems of extrinsic geometry of foliations, which, roughly speaking, describes how leaves (or single submanifolds) are located in the ambient pseudo- Riemannian space. We discuss the following topics with the mixed scalar curvature: integral formulas and splitting of foliations, prescribing the mixed curvature of foliations, and variations of functionals defined on foliations, which seem to be central in extrinsic geometry.

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Authors and Affiliations

  1. University of Haifa, Haifa, Israel

    V. Yu. Rovenski

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  1. V. Yu. Rovenski
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Correspondence to V. Yu. Rovenski.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 179, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.

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Rovenski, V.Y. Problems of Extrinsic Geometry of Foliations. J Math Sci 276, 391–399 (2023). https://doi.org/10.1007/s10958-023-06755-w

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