Open AccessLifting semi-invariant submanifolds to distribution of almost contact metric manifolds
Author(s) -
А. В. Букушева
Publication year - 2020
Publication title -
differencialʹnaâ geometriâ mnogoobrazij figur
Language(s) - English
Resource type - Journals
eISSN - 2782-3229
pISSN - 0321-4796
DOI - 10.5922/0321-4796-2020-51-5
Subject(s) - mathematics , connection (principal bundle) , submanifold , manifold (fluid mechanics) , metric connection , pseudo riemannian manifold , pure mathematics , statistical manifold , invariant (physics) , volume form , morphism , distribution (mathematics) , levi civita connection , mathematical analysis , fundamental theorem of riemannian geometry , hermitian manifold , ricci curvature , geometry , information geometry , mathematical physics , curvature , scalar curvature , mechanical engineering , engineering
Let M be an almost contact metric manifold of dimension n = 2m + 1. The distribution D of the manifold M admits a natural structure of a smooth manifold of dimension n = 4m + 1. On the manifold M, is defined a linear connection that preserves the distribution D; this connection is determined by the interior connection that allows parallel transport of admissible vectors along admissible curves. The assigment of the linear connection is equivalent to the assignment of a Riemannian metric of the Sasaki type on the distribution D. Certain tensor field of type (1,1) on D defines a so-called prolonged almost contact metric structure. Each section of the distribution D defines a morphism of smooth manifolds. It is proved that if a semi-invariant submanifold of the manifold M and is a covariantly constant vector field with respect to the N-connection , then is a semi-invariant submanifold of the manifold D with respect to the prolonged almost contact metric structure.