Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 179, Pages 41–49
DOI: https://doi.org/10.36535/0233-6723-2020-179-41-49 (Mi into625) 		 
Problems of extrinsic geometry of foliations

V. Yu. Rovenskiĭ

University of Haifa
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DOI: https://doi.org/10.36535/0233-6723-2020-179-41-49
Abstract: This survey is devoted to particular problems of extrinsic geometry of foliations, which, roughly speaking, describes how leaves (or single submanifolds) are located within 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.
Keywords: extrinsic geometry, pseudo-Riemannian metric, affine connection, foliation, mixed scalar curvature, integral formula, variation.
Document Type: Article
UDC: 514.76
MSC: 53C12, 53C21
Language: Russian
Citation: V. Yu. Rovenskiǐ, “Problems of extrinsic geometry of foliations”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 179, VINITI, Moscow, 2020, 41–49
Citation in format AMSBIB
\Bibitem{Rov20}
\by V.~Yu.~Rovenski{\v\i}
\paper Problems of extrinsic geometry of foliations
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 179
\pages 41--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into625}
\crossref{https://doi.org/10.36535/0233-6723-2020-179-41-49}
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