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Results tagged with dg.differential-geometry
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user 74747
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
4
votes
1
answer
1k
views
Decomposition of pullback metric
Let $(M^3,g)$ be a complete riemannian manifold and $\Sigma ^2\subset M^3$ a embedded minimal compact surface. Consider the immersion $\phi: \Sigma \times [0,\varepsilon)\to M$ given by
$$\phi(p,t)=\ …
- 183
0
votes
2
answers
217
views
Normal variation of embedded surfaces [closed]
Let $M^3$ be a complete riemannian manifold and $\Sigma ^2\subset M^3$ a embedded minimal compact surface. Consider the normal variation $\phi: \Sigma \times \Bbb{R}\to M$ given by
$$\phi(p,t)=\exp_p …
- 183
0
votes
0
answers
117
views
Fundamental theorem for real submanifolds into complex space forms
It is a well-known result that Gauss, Codazzi and Ricci equations are necessary and suficiently conditions to guarantee the existence of an isometric immersion of a given $n$-dimensional real Riemanni …
- 183