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Results tagged with riemannian-geometry
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user 5659
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.
8
votes
Property of distance function with "smoothly" varying Riemannian metrics
About the formulation, I would see such a family as a smooth map from $[0,1]$ to the space of smoooth sections of $S^2T^*M$ which lands in the open set of sections with values in positively definite f …
- 2,727
7
votes
Accepted
Curvature of varieties of log general type
No, this is not true, even for $\Delta=\emptyset$. If $X$ admits a Kähler metric with negative holomorphic bisectional curvature, then so do all its subvarieties; in particular, all its subvarieties a …
- 2,727
3
votes
Unique Kahler-Einstein metric $g$ with $\mathrm{Ricc}(g)=-g$ when first Chern class $C_1(M)<...
so here I guess $M$ is a compact Kähler manifold.
Thanks to Yau theorem, we know that there exists a unique Kähler metric $h$ in each Kähler cohomology class such that $\mathrm{Ric}(h)=-g$ (more gene …
- 2,727