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Results tagged with dg.differential-geometry
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user 496823
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
8
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1
answer
418
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Existence of a special vector field on Riemannian manifolds?
In a Riemannian Manifold $(M,g)$ a vector field $X$ is said to be Killing vector field if $L_X g$=0 and is said to be conformal if $L_X g= fg$ for some smooth real function $f$ on $M$.
Also, the notio …
1
vote
2
answers
133
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Does this special vector field affect on sectional curvature?
We have a nowhere vanishing vector field $X$ on a Reimannian manifold $(M,g)$, such that $\mathcal{L}_X g=2\alpha X^\flat \otimes X^\flat$ for a constant non zero $\alpha$. So, for every vector fields …