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Results tagged with riemannian-geometry
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user 36688
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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The tensor product of two Fredholm operators
What can be said about the tensor product $T\otimes S$ of two Fredholm operators $T:X_1\to Y_1$ and $S:X_2 \to Y_2$ where $X_1,X_2,Y_1, Y_2$ are Banach spaces and tensor product of operat …
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Is a Riemannian submersion a harmonic map?
Is every Riemannian submersion necessarily a Harmonic map? If not under what condition that is true?
The motivation: the linear part of a Riemannian submersion is the direct sum og an isometry a …
- 35.5k
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Is a Riemannian submersion a harmonic map?
I just realize that the answer is negative:
Radu Pantilie, Some remarks on harmonic Riemannian submersion, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série T …
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Is isoperimetric hypersurface unique up to homeomorphism?
Is there a Riemannian structure on $\mathbb{R}^n $with two non homeomorphic compact hypersurfaces $M,N$ such that both satisfy the isoperimetric inequality. I precisely meanthe following:
$$\el …
- 356
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Horizontal knots on 3 sphere
Motivation: First I present my motivation for this question but this motivational part is not my main question.
I participated in a talk on knot theory. Then I presented the following …
- 28.2k
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Are all linear vector fields geodesible vector fields?
I had already asked this question in MSE then I ask here at MO.
Assume that $A\in M_n(\mathbb{R})$ is a non singular matrix.
Is the flow of the linear vector field $X'=AX$ a geodesible flow on $\ma …
- 356
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The Frobenius integrability of distrbution and Hyers–Ulam–Rassias stability
Let $M$ be a compact Riemannian manifold. The norm of vector fields are computed with respect to the metric. Moreover for every distribution $D$, the orthogonal projection on $D$ is den …
- 356
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A Lie group whose Lie algebra is equal to (the Lie algebra? of )all functions with fibrewise...
Let $M$ be a Riemannian manifold. We denote by $\mathfrak{g}$ the space of all smooth function $f:TM\to \mathbb{R}$ with fibre wise polynomial growth. Is it a Lie algebra wrt the Poisson bracket …
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Hamiltonian approach to Einstein manifold theory
Let $(M,g)$ be a Riemannian manifold. So $TM$ has a natural structure of a symplectic manifold. The zero section is denoted by $Z$.
We define a Hamiltonian on $T^0 M=TM\setminus Z$ via $$ …
- 356
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Einstein structure and the quotient (group)$\frac{\operatorname{Ricc}_g}{\operatorname{Iso}_g}$
$\newcommand{\Ric}{\operatorname{Ric}}\newcommand{\Iso}{\operatorname{Iso}}$Let $(M,g)$ be a Riemannian manifold with corresponding LC connection and Ricci tensor.
Is there an obvious description of …
- 356
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Einstein metrics on the tangent bundle
Some Particular cases are explained in Papaghiuc - On an Einstein structure on the tanent bundle of a space form.
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Dynamical obstruction for a vector field to have a Harmonic divergence
Let $(M,g)$ be an analytic Riemannian manifold and $X$ be an analytic vector field on $M$. Can we always have a volume form $\Omega$ such that $\operatorname{Div}_{\Omega} X$ is a harmonic …
- 356
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A (possible) Lie algebra extension of the Lie algebra of a foliation
Motivation: The aim of this post is to extend the Lie algebra of a foliation to a bigger Lie algebra. We assume that a manifold $M$ is foliated by compat leaves. The Lie algebra of the foliation is th …
- 356
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Invariants associated to a principal bundle whose total space is a symplectic manifold acted...
The following question - proposal came to my mind about 4 years ago but I did not find any solution to this question and did not find any answer via e-personal comunication with some research …
- 356
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Geometric interpretation for a connection whose corresponding distribution generates the who...
Let we have a connection on a manifold $M$ so it is considered as a distribution on the tangent bundle $TM$ of $M$. The integrability of this distrbution is equivalent to flatness of the connection. …
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