Levy [11] had proved that a second order symmetric parallel non singular tensor on a space of constant curvature is a constant multiple of the metric tensor. Sharma [6] has proved that second order parallel tensor in a Kaehler Space of constant holomorphic sectional curvature is a linear combination with constant coefficients of the Kaehlerian metric and the fundamental 2-form. In this paper, w...

Let g be the Lie algebra of a compact Lie group and let θ be any automorphism of g. Let k denote the fixed point subalgebra g . In this paper we present LiE programs that, for any finite dimensional complex representation π of g, give the explicit branching π|k of π on k. Cases of special interest include the cases where θ has order 2 (corresponding to compact Riemannian symmetric spaces G/K), ...

In this paper we shall prove two theorems (Stability Theorem, Local Torelli Theorem) for symplectic varieties. Let us recall the notion of a symplectic singularity. Let X be a good representative of a normal singularity. Then the singularity is symplectic if the regular locus U of X admits an everywhere non-degenerate holomorphic closed 2-form ω where ω extends to a regular form on Y for a reso...