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University lecturer.

Nov
17
comment Gaussian Curvature of Exponentiated 2-Planes
Anton: you expect what is true?
Nov
17
comment Gaussian Curvature of Exponentiated 2-Planes
Okay, thanks Anton. It would be nice to know what happens in the case of compact symmetric spaces.
Nov
17
accepted Gaussian Curvature of Exponentiated 2-Planes
Nov
17
awarded  Popular Question
Nov
15
comment Gaussian Curvature of Exponentiated 2-Planes
Anton, what if I add the condition that the manifold $M$ is compact? I'm specifically interested in the case of Riemannian symmetric spaces of compact type.
Nov
15
revised Gaussian Curvature of Exponentiated 2-Planes
deleted 2 characters in body
Nov
15
asked Gaussian Curvature of Exponentiated 2-Planes
Sep
24
awarded  Autobiographer
Sep
23
comment Tori in Compact Riemannian Symmetric Spaces
@IgorBelegradek: Thanks for the reference.
Sep
22
comment Tori in Compact Riemannian Symmetric Spaces
I guessed that's what you meant but just wanted to make sure. Thanks again for the nice answer.
Sep
22
comment Tori in Compact Riemannian Symmetric Spaces
Thanks for the answer Robert but there's something puzzling me. The flats you describe above need not be tori, right? For example, if we have a symmetric space of noncompact type then the exponential map is a diffeomorphism and so the space can't contain a torus. Have I misunderstood something?
Sep
22
accepted Tori in Compact Riemannian Symmetric Spaces
Sep
21
asked Tori in Compact Riemannian Symmetric Spaces
Jul
2
awarded  Curious
Jun
24
comment Decomposition of Lie subspaces
I can check my claim with $S^7=Spin(7)/G_2$.
Jun
24
comment Decomposition of Lie subspaces
For a symmetric space, the canonical connection has zero torsion and so $\frak{m}$$_1=0$. So the result is trivially true, isn't it?
Jun
24
comment Decomposition of Lie subspaces
Let me be a little more specific. Is it possible to view $\frak{m}$$_1$ as the Lie algebra of some subgroup of $G$?
Jun
23
comment Decomposition of Lie subspaces
I think this answers my question, Jose. Thanks. However, I was wondering whether there were any results of this nature in the literature. The Lie group result is well-known and I would have thought that it was generalized to reductive spaces.
Jun
23
accepted Decomposition of Lie subspaces
Jun
23
comment Decomposition of Lie subspaces
@JoséFigueroa-O'Farrill What I meant was $T_o(\frak{m}_1,\frak{m}_1)\ne 0$. Also, in the decomposition, $\frak{m}_0$ is a subspace and $\frak{m}_1$ is a semi-simple subalgebra of $(\frak{m}$,$T_o)$.