New posts in riemannian-geometry

Proof that every Riemannian geodesic is locally minimizing

differential-geometry riemannian-geometry

Any compact embedded $2$-dimensional hypersurface in $\mathbb R^3$ has a point of positive Gaussian curvature

riemannian-geometry

What does $ds^2$ mean and how does it specify a metric?

riemannian-geometry

Bound of $D\exp$ in Riemannian manifold with $|\text{sec} M| \leq K$ and $\text{inj}M \geq i_0$

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Control the sectional curvature

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$ a+b+c=0,\ a^2+b^2+c^2=1$ implies $ a^4+b^4+c^4=\frac{1}{2}$

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Worst case examples of non-differentiability of the Riemannian distance function

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How to define a Riemannian metric in the projective space such that the quotient projection is a local isometry?

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Can speed be defined for a parametrized but irregular curve in a Riemannian manifold?

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On a definition of manifold

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Geodesic convexity and the 2nd fundamental form

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Holonomy of Lie groups

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The Riemannian Distance function does not change if we use smooth paths?

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Riemannian metric making a given function harmonic

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Product of Riemannian manifolds?

riemannian-geometry

Explicit example of a compact manifold of dimension $>2$ with strictly negative sectional curvature

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Is $ds$ a differential form?

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How can I understand the three-dimensional space forms?

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Isometries of $\mathbb{S}^n$

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How to find the Riemannian Distance on the Sphere $S^n\subset \Bbb{R}^{n+1}$

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