49

Answers

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4

Real analytic submanifolds of $\mathbb{R}^{n}$

9

Noteworthy achievements in and around 2010?

2

Does every smoothly embedded surface $\mathbb{R}^3$ inherit a natural complex structure, and if so, which one?

4

Rank two vector bundles on a curve of genus two

4

Given a vector field all of whose integral curves are closed, is the period a smooth function?

3

Tweetable way to see that Willmore energy is Möbius invariant?

10

First nonzero eigenvalue of the Laplacian on the submanifold

9

Adjoint of a Connection Using the Hodge Map?

4

A question on deformations of Theta divisor in the Jacobian of a complex curve

1

Is there a complete classification of constant mean curvature surfaces?

7

Willmore minimizers for genus $\geq 2$

1

complex vector bundles and curvature

2

What are some geometric reasons why a Dirac operator would have a gap in its spectrum?

1

Is there a coordinate-free proof of the hamiltonian character of the geodesic flow?

2

Is there a sheaf theoretical characterization of a differentiable manifold?

4

space of geodesics

2

Decomposition of straight line between points on a manifold

-1

Characterization of certain curves of $\mathbb{R}^2$

1

Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature

3

Reference for openness of stable locus of holomorphic family of vector bundles on a compact riemann surface.

1

equivariant index of Dirac Operator on $S^{2}$

1

Quotient Surface of A Hyperelliptic Involution

2

How do I see sectional curvature in the principal bundle (or in Cartan’s) approach to riemannian geometry?

4

Torus minimizer of Willmore energy

1

Twisting Spinor Bundles with Line Bundles

9

Dirac’s Original Operator and the Hodge--Dirac Operator

0

What is known about Higgs bundles with sections?

0

Is there an intrinsic way to define the group law on Abelian varieties?

4

A equivalent definition of abelian variety

12

Proofs that require fundamentally new ways of thinking