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15
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Does a Riemannian metric allow definition of a tangent vector's length?

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#riemannian-geometry
34
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Choosing a Riemannian-metric such that a submanifold $V \subset \mathbb{R}^n$ is totally geodesic.

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#differential-geometry #riemannian-geometry #smooth-manifolds
211
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Calculation: vector field commutes with Laplacian iff it is Killing

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#riemannian-geometry #tensors
69
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Basic notation for a PDE

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#partial-differential-equations #manifolds #riemannian-geometry #spheres #fluid-dynamics
966
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Why are parallelizable manifolds called parallelizable?

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#differential-geometry #riemannian-geometry #smooth-manifolds
59
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Divergence of Yamabe soliton

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#differential-geometry #riemannian-geometry
163
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Ricci curvature is symmetric bilinear form: Why $T_pM \times T_pM \to T_pM$ and not $T_pM \times T_pM \to \mathbb R$?

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#differential-geometry #riemannian-geometry #tensors #vector-bundles #curvature
45
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What does it mean if $\text{Ric} =0$

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#riemannian-geometry
135
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Symmetry of the (Riemann) curvature tensor of the Riemannian connection: $\nabla_{\nabla_Y Z}W = \nabla_Y(\nabla_Z W)$?

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#differential-geometry #riemannian-geometry #tensors #curvature #connections
123
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Can anyone tell me from which book is this chapter about the Bryant soliton?

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#differential-geometry #reference-request #riemannian-geometry #ricci-flow
485
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Are harmonic functions always real analytic?

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#reference-request #riemannian-geometry #harmonic-functions #regularity-theory-of-pdes #elliptic-operators
42
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$\frac{D}{dt}(u_t(\gamma_t))=(\partial_tu+\nabla_{u_t}u_t)\circ\gamma_t$?

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#calculus #geometry #riemannian-geometry #partial-derivative
65
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Relationship between Levi Civitá connections

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#riemannian-geometry #smooth-manifolds #isometry #connections #pullback
342
Views

what is the motivation of Hamilton-DeTurck Ricci flow?

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#differential-geometry #partial-differential-equations #riemannian-geometry #ricci-flow
176
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Is Riemann curvature tensor defined for the Riemannian connection?

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#differential-geometry #riemannian-geometry #vector-bundles #curvature #connections

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