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Authors
Affiliations
1 Department of Mathematics, Indian Institute of Technology, Bombay, IN
Source
Journal of the Ramanujan Mathematical Society, Vol 25, No 2 (2010), Pagination: 147-167
Abstract
Consider a linear action of a Lie group G on the matrix space Mn (𝔽). Each orbit space is then an embedding of a homogeneous space in the euclidean space M ⊂ Mn (𝔽). In this paper, we give a characterization of all linear maps on Mn (𝔽) which when restricted to M define a Morse function on M, for the case M is one of the orthogonal groups O(n, 𝔽), the Stiefel manifolds 𝕍k (ℝn) and the flag manifolds F(n1, n2, . . . , nr).