Commun. Korean Math. Soc. 2015; 30(3): 253-267
Printed July 31, 2015
https://doi.org/10.4134/CKMS.2015.30.3.253
Copyright © The Korean Mathematical Society.
Jaehyun Hong
Seoul National University
Given a complex submanifold $M $ of the projective space $ \mathbb P(T)$,the hyperplane system $R$ on $M$ characterizes the projective embedding of $M$ into $\mathbb P(T)$ in the following sense: for any two nondegenerate complex submanifolds $M \subset \mathbb P(T)$ and $M '\subset \mathbb P(T')$, 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
MSC numbers: Primary 32Mxx, 53Cxx
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