Normal connection in the geometry of normalized submanifolds of affine space

A survey is given of results concerning the study of the structure of a normalized subraanifold of affine space with the help of a normal connection.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.93–107, 1989.     

Normal connection and submanifolds with parallel normal fields in a space of constant curvature

A summary account of the cycle of papers of the authors on submanifolds of a space of constant curvature with a parallel field of p-directions, also containing some new results. In the concluding section there is given a survey of papers on submanifolds of a Riemannian manifold using the concept of normal connection.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 12, pp. 3–30, 1981.     

A class of submanifolds in V c n with parallel p-dimensional subbundle of the normal bundle

The local structure of a submanifold V^m is studied for which the focal surface F of a subbundle N^p has s distinct components with multiplicities p₁, . . ., p_s(p₁ + . . . + p_s = m), and the focal surface of the subbundle N^n-m-p has no multiple components.Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 477–483, October, 1977.     

A submanifold in Pn with parallel normal subbundle which is normalized in the sense of norden

The concept of a p-dimensional parallel subbundle of the normal bundle of a submanifold V^m of n-dimensional protective space Pⁿ normalized in the sense of Norden [1] is introduced. The local structure of such manifolds is studied. The structure is also investigated of submanifolds V^m which have normal subbundles with a flat projective connection. Their structure is closely related with the structure of tangentially degenerate submanifolds [2, 3] and submanifolds admitting a dual normalization [4].Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 649–662, November, 1977.I express my sincere gratitude to M. A. Akivis and Yu. G. Lyumista for valuable comments which they made in duscussing the results of this paper.     

A connection in normal bundles of normalized submanifolds Vm in Pn

This paper contains a survey of papers on the theory of connections arising on normal bundles of multidimensional surfaces in projective space.Translated from Itogi Nauki i Tekhniki. Problemy Geometrii, Vol. 10, pp. 55–74, 1978.