Questions tagged [dg.differential-geometry]
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
8,907 questions
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compactly supported harmonic functions [closed]
Do a significant class of compactly supported smooth functions u on Ω⊂Rn such that Δu≥0 exist?
Thanks!
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Loop space of manifold [closed]
Question A: The free loop space of a manifold is also a manifold?
Question B: The free loop space of an algebraic variety is also a algebraic variety ?
Are these questions asked or answered anywhere ...
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What is a coordinate less definition of differentiable manifolds
![enter image description here]
From Clifford algebra to geometric calculus by d. Hestenes
https://en.wikipedia.org/wiki/Universal_geometric_algebra
The attempt above is to have the base manifold ...
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Does a coarser topology lead to a non-Hausdorff topological manifold? [closed]
Take a topological manifold $M$. Suppose one considers a strictly coarser topology than the manifold topology. Can such topology result in a non-Hausdorff topological manifold?
NOTE: PLEASE avoid the ...
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Symplectic forms and 1-forms [closed]
Suppose we have a real symplectic manifold $(M,\omega)$. Under what conditions can we find a global 1-form $\alpha$ such that $\omega = \alpha \wedge\alpha$?
Obviously there are some simple ...
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Constructing a new manifold with a germ of manifold [closed]
Given a germ of manifolds and compatible Riemannian metrics, can we construct a new Hausdorff manifold using the exponential map?
A germ of manifolds at a point $m$ is a series of manifolds $U_i$ ...
user176431
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Gaussian curvature and mean curvature. [closed]
Define Gaussian curvature for a nonorientable surface. Can you define mean curvature for a nonorientable surface?
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