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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### Can the metric be reconstructed (up to scaling) from knowing the conjugate points?

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### Continuous deformation of harmonic forms under a change of metric

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### Immersions of the hyperbolic plane

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### Flatness in a neighborhood of a point condition

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### Totally geodesic submanifold of codimension 1 in noncompact Riemannian manifold

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### Totally geodesic submanifold of codimension 1

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### inverse of sobolev riemannian metric still sobolev?

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### Characteristics of Poincare's ball model (of hyperbolic spaces)

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### Can we specify the value of harmonic forms at a point?

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### Contractibility of balls in Alexandrov spaces

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### Higher order variations of Riemannian geodesics

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### Focal point (Definition ) [closed]

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### $\ell_p$ geodesic distance on smooth Riemannian manifold and Logarithmic Sobolev Inequalities

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### A conformal map whose Jacobian vanishes at a point is constant?

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### Is Serre duality related to Pontryagin duality?

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### Isoperimetric inequality inside a regular polygon

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### Reference request: Recovering a Riemannian metric from the distance function

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### Codimension reduction for developable Euclidean submanifold

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### Function is $L^p$-integrable for $p >1$ [Kähler Geometry]

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### Atiyah-Patodi-Singer for manifolds with cusps

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### How do we compute the trace over the matrix logarithm $\log((\sigma_2 \otimes I_{n/2})^T\cdot\Omega)$?

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### Counter-examples to the higher dimensional statement of the half-space theorem

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### A sufficient condition for isometrically embedding of manifolds in the Euclidean space they have already sat

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### Does a map which preserve harmonic forms preserve co-closed forms (locally)?

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### Generalizing the Madsen-Weiss Theorem via the scanning map $\mathscr{C}(M,\mathbb{R}^{\infty})\to\Omega^{\infty}AG^+_{\infty,d}$

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### Desingularization of the zero section of $TM$ as the manifold of singularities of the geodesic flow

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### Unique factorisation of prime geodesics?

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### Can we define a normal vector field on the level sets of the distance function?

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### Hausdorff convergence of submanifolds in $\mathbb{S}^m$

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### Smoothness of a curve vs. smoothness of the squared distance from the curve to points on Riemann manifolds

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### Is the development map in Hyperbolic geometry related to development in Cartan geometry?

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### metric with curvature bounded in $L^2$

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### What is the weakest negative curvature condition ensuring a manifold is a $K(G,1)$?

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### Projection of a ball in the ambient space to a manifold

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### Does a spectral gap lift to covering spaces?

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### Holonomy groups of compact Riemannian symmetric spaces

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### Heat kernel and convergence

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### Conformal factors and light rays

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### A kind of converse to the Hopf theorem on ergodicity of geodesic flow in negative curvature

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### Discrete approximation of Minkshisundaram-Pleijel zeta function?

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### Spin-H structures

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### Isometries along the normalized Ricci flow

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### Does the zeta regularized Laplacian determinant measure the volume of some parameter space? How many “spanning trees” on a manifold?

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### There is no metric of positive sectional curvature on $\mathbb{S}^2\times\mathbb{S}^2$.

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### What is $e^{- \zeta_{\Delta} '(0)}$ for a $\Delta$ the Laplacian of a manifold?

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### Ergodicity of geodesic flow in negative curvatutre as a possible obstruction for consideration of limit cycles as closed geodesics(4)

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### Must a manifold covered by $ S^n $ admit a metric of constant positive sectional curvature?

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### A foliation of the cylinder by closed geodesics of the same length when the metric is complete but non flat

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### Bochner formula in different forms

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