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We give a precise characterization for when a compact CR-solvmanifold is CR-embeddable in a complex Kähler manifold. Equivalently this gives a non-Kähler criterion for complex manifolds containing CR-solvmanifolds not satisfying these conditions. This paper is the natural continuation of...
In this paper, we classify the real hypersurfaces in a non-flat complex space form with η-parallel shape operator.
For two complex vector bundles admitting a homomorphism with isolated singularities between them, we establish a Poincaré–Hopf type formula for the difference of the Chern character numbers of these two vector bundles. As a consequence, we extend the original Poincaré–Hopf index formula to the...
A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tame extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt group of graded quadratic forms over the graded ring associated to...
In this paper, we prove a ‘cut-by-curves criterion’ for an overconvergent isocrystal on a smooth variety over a field of characteristic p > 0 to extend logarithmically to its smooth compactification whose complement is a simple normal crossing divisor, under certain assumption. This is a p-adic...
We show that a compact Ricci soliton is rigid if and only if the Weyl conformal tensor is harmonic. In the complete noncompact case we prove the same result assuming that the curvature tensor has at most exponential growth and the Ricci tensor is bounded from below.
The length of a field is the smallest integer m such that any totally positive quadratic form of dimension m represents all sums of squares. We investigate this field invariant and compare it to others such as the u-invariant, the Pythagoras number, the Hasse number, and the Mordell function...
Branched covers of orbit cylinders are the basic examples of holomorphic curves studied in symplectic field theory. Since all curves with Fredholm index one can never be regular for any choice of cylindrical almost complex structure, we generalize the obstruction bundle technique of Taubes for...
Given a compact four-dimensional smooth Riemannian manifold (M,g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero. Using integral methods, we prove global existence and convergence for the...
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