On differential-geometric structures on submanifolds of a manifold with an almost quaternionic structure
type: Item
instance of: scholarly article
title: On differential-geometric structures on submanifolds of a manifold with an almost quaternionic structure
zbMATH Open document ID: 0835.53066
author: R. F. Dombrovs'kyj
published in: Russian Mathematics
publication date: 1995-11-05T00:00:00Z
review text: A manifold \({\mathcal M}_n\) with a pair \((\varphi, \psi)\) of endomorphisms of the tangent bundle \(T {\mathcal M}_n\) for which there hold relations \(\varphi^2 = \psi^2 = -\text{id}\), \(\varphi \circ \psi + \psi \circ \varphi = 0\) is called a manifold with an almost quaternionic structure \({\mathcal M}_n(\varphi, \psi)\). The derivation equations of a normal rigging submanifold \({\mathfrak M}_m \subset {\mathcal M}_n (\varphi, \psi)\) are given. The intersections \({\bigwedge_x}_\varphi = T_x ({\mathcal M}_m) \cap \varphi T_x ({\mathfrak M}_m)\), \({\bigwedge_x}_\psi = T_x ({\mathfrak M}_m) \cap \psi T_x ({\mathfrak M}_m)\), \(x \in {\mathfrak M}_m\) are constructed. If these intersections are not empty, then the submanifold \({\mathfrak M}_m\) is said to be generic. The special classes of generic submanifolds are indicated.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 795250
zbMATH Keywords: generic submanifold
zbMATH Keywords: almost quaternionic structure
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 795250