Equiaffine immersions of codimension two with flat connection and one-dimensional Weingarten mapping
Анотація
In the paper we study equiaffine immersions f:(Mn,∇)→Rn+2 with flat connection ∇ and one-dimensional Weingarten mapping. For such immersions there are two types of the transversal distribution equiaffine frame.
We give a parametrization of a submanifold with the given properties for both types of equiaffine frame. The main result of the paper is contained in Theorems 1, 2 and Corollary 1: Let f:(Mn,∇)→(Rn+2,D) be an affine immersion with pointwise codimension 2, equiaffine structure, flat connection ∇, one-dimensional Weingarten mapping then there exists three types of its parametrization:
(i)
→r=g(u1,…,un)→a1+∫→φ(u1)du1+n∑i=2ui→ai;
(ii) →r=(g(u2,…,un)+u1)→a+∫v(u1)→η(u1)du1+n∑i=2ui∫λi(u1)→η(u1)du1;
(iii) →r=(g(u2,…,un)+u1)→ρ(u1)+∫(v(u1)−u1)d→ρ(u1)du1du1+n∑i=2ui∫λi(u1)d→ρ(u1)du1du1.
Посилання
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Авторське право (c) 2023 O. O. Shugailo

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