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Results tagged with riemannian-geometry
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user 74747
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
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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 …
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Isometric immersions and metrics in the same conformal class
Let $\phi:\Sigma^2\to M^3$ an conformal isometric immersion into a Riemannian 3-manifold $(M,g)$.
I would like to know what kind of informations is preserved (about the immersion) when we change $g$ …
- 6,825
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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
$$\phi(p,t)=\ …
- 39.1k
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Normal variation of embedded surfaces [closed]
Let $M^3$ be a complete riemannian manifold and $\Sigma ^2\subset M^3$ a embedded minimal compact surface. Consider the normal variation $\phi: \Sigma \times \Bbb{R}\to M$ given by
$$\phi(p,t)=\exp_p …
- 7,197