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Characterization of Hermitian symmetric spaces by fundamental forms. (English) Zbl 1053.32012

Following Y. Se-Ashi [Hokkaido Math. J. 17, No. 2, 151–195 (1988; Zbl 0664.34018)], the authors first recall the definition of the fundamental forms for a complex submanifold in the projective space. After proving an invariant-theoretic result concerning the fundamental forms of the Hermitian symmetric spaces, the authors characterize an equivariantly embedded Hermitian symmetric space in a projective space by its fundamental forms as a local submanifold. The proof is reduced to the vanishing of certain Spencer cohomology groups, which is checked by Kostant’s harmonic theory for Lie algebra cohomology.

MSC:

32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
53B25 Local submanifolds
14M15 Grassmannians, Schubert varieties, flag manifolds

Citations:

Zbl 0664.34018
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References:

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