# Tagged Questions

A branch of differential geometry dealing with Riemannian manifolds. *Riemannian manifolds* are smooth manifolds with an inner product smoothly attached to the tangent space of each point. Usually, Riemannian geometry focuses on the notions of distance, curvature, and shape. Consider using this tag ...

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### Find a surface that has positive constant curvature that is not open subset of sphere

Can some one find a surface that has positive constant curvature that is not open subset of sphere. I know every connected and compact surface with positive constant curvature is sphere. I need ...
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### Local expression of hermitian metric

I have really hard times reading Zheng's Complex Differential Geometry and I find the following sentence especially baffling (sec. 7.4, page 170): "Let $M^n$ be a complex manifold. A Hermitian metric ...
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### Index notation.

I have a very basic question concerning index notation, normally used in physic papers. I have never used index notation and it is very difficult to me to translate from index free notation, even in ...
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### How does the Schrodinger's potential transformer if the metric conformally transformers?

Given Schrodinger's equation $$(-\nabla^2+V)\psi=E\psi$$ and the conformal transformation $\tilde{g}_{mn}=e^{2\phi}g_{mn}$, how does the Schrodinger's potential $V$ transformer if the metric ...
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### Diameter of the Grassmannian

Just an interesting question that came to my mind while studying(!): Since the Grassmannian $G(k,\mathbb{C}^n)$ is a compact manifold, what do we know about its diameter? Do we know any estimate? ...
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### Riemannian metric of $3$-sphere

I know this probably seems like a dumb question, I have parametrised part of the unit $3$-sphere with $(x,y,z)\to (x,y,z,(1-(x^2+y^2+z^2))^{\frac{1}{2}})$ and now I'm trying to calculate the ...
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### What is the formal name for the conformal laplacian?

\begin{align} L=R-4\dfrac{n-1}{n-2}\nabla^k\nabla_k \end{align} What is the formal name for $L$? I have seen it referred to as the conformal laplacian, however I thought I once read $L$ with a formal ...