ON DIFFERENTIAL INVARIANTS OF HYPERPLANE SYSTEMS ON NONDEGENERATE EQUIVARIANT EMBEDDINGS OF HOMOGENEOUS SPACES

Title & Authors
ON DIFFERENTIAL INVARIANTS OF HYPERPLANE SYSTEMS ON NONDEGENERATE EQUIVARIANT EMBEDDINGS OF HOMOGENEOUS SPACES
HONG, JAEHYUN;

Abstract
Given a complex submanifoldM of the projective space $\small{\mathbb{P}}$(T), the hyperplane system R on M characterizes the projective embedding of M into $\small{\mathbb{P}}$(T) in the following sense: for any two nondegenerate complex submanifolds $\small{M{\subset}\mathbb{P}}$(T) and $\small{M^{\prime}{\subset}\mathbb{P}}$(T), there is a projective linear transformation that sends an open subset of M onto an open subset of M if and only if (M,R) is locally equivalent to (M, R). Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.
Keywords
homogeneous spaces;fundamental forms;
Language
English
Cited by
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