Geodesic
Problems of extrinsic geometry of foliations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 179 (2020), pp. 41-49

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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, mixed scalar curvature, integral formula
Mots-clés : foliation, variation. 
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     author = {V. Yu. Rovenskiǐ},
     title = {Problems of extrinsic geometry of foliations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {41--49},
     publisher = {mathdoc},
     volume = {179},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_179_a6/}
}
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V. Yu. Rovenskiǐ. Problems of extrinsic geometry of foliations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 179 (2020), pp. 41-49. http://geodesic.mathdoc.fr/item/INTO_2020_179_a6/