# Tagged Questions

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### Geometric meaning of the black hole horizon

It is widely accepted that the singularity of the Schwarzschild metric at the event horizon is purely an artifact of the coordinates and no physical singularity exists at the horizon. However, as ...
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### How to prove that all smooth vector bundles on a given vector bundle are the pull back of a vector bundle on the base [migrated]

Recently, during a conversation, I heard about the result (previously mentioned also here on MO), whose statement is reported below. Not having the specific background necessary to reconstruct a proof ...
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### Complex structures on Riemann surfaces

This is cross posted from math.SE: http://math.stackexchange.com/q/876432/9 Let $M$ be a Riemann surface and $[\alpha] \in H^{0,1}(M; T^{1,0} M) \simeq (H^0(M;K^2))^*$. Considering $\alpha$ as a map ...
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### nth term in the Baker-Campbell-Hausdorff formula

I am trying to prove a result for which I need the nth term of the Baker-Campbell-Hausdorff formula. I came at this particular result (which is not of significance for the question, but mentioning for ...
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### Complex geometry text/research introduction for the analyst

To give some background, I am mainly an analyst trained in harmonic/functional and do work on geometric pde's and spectral multipliers. Of late, I am trying to learn more about (research level) ...
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### Structure of the zero set of analytic maps (Lojasiewicz’s Structure Theorem for Varieties)

The Lojasiewicz’s Structure Theorem for Varieties states that for $\Phi:\mathbb{R}^n\rightarrow \mathbb{R}$ real analytic with $\Phi(0)=0$ the set $\Phi^{-1}(0)$ is locally a union of subvarieties of ...
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### A geometric characterization of smooth points of a complex algebraic variety

Let $X^m\subset \mathbb{C}^n$ be an irreducible $m$-dimensional complex algebraic subvariety. Let $\mathbb{C}^n$ be equipped with the standard Hermitian metric. Fix an arbitrary point $p\in X$. Let ...
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### The integral of torsion

I found the following * exercise(exercise *9) in page 407 of the book of Do Carmo "Differential geometry of curves and surfaces". This problem is a classical theorem which is referenced in the book ...
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### Bundles over Function Spaces

Is there any reference on bundles over function spaces? In particular, I am interested in Banach-bundles over function spaces like $W^{k,r}(M)$, where $M$ is a Riemannian manifold. Separable ...