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pro vyhledávání: '"53C27"'
Autor:
Mathews, Daniel V., Varsha
This article is an exposition and elaboration of recent work of the first author on spinors and horospheres. It presents the main results in detail, and includes numerous subsidiary observations and calculations. It is intended to be accessible to gr
Externí odkaz:
http://arxiv.org/abs/2412.10862
Autor:
Mathews, Daniel V., Varsha
We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski space; and horospheres in 4-dimensional hyperbolic space decorated wi
Externí odkaz:
http://arxiv.org/abs/2412.06572
Autor:
Fine, Joel, Ghosh, Partha
Starting with an $n$-dimensional oriented Riemannian manifold with a Spin-c structure, we describe an elliptic system of equations which recover the Seiberg-Witten equations when $n=3,4$. The equations are for a U(1)-connection $A$ and spinor $\phi$,
Externí odkaz:
http://arxiv.org/abs/2411.09348
In the complete hyperbolic structure on the complement of the figure eight knot, we determine the set of lambda lengths from the maximal cusp to itself. Using the correspondence between spinors and spin-decorated horospheres, we show that these lambd
Externí odkaz:
http://arxiv.org/abs/2411.06368
Given a finitely generated discrete group {\Gamma}, we construct for any admissible crossed product completion and for any metrizable finite dimensional compact {\Gamma}-space X, a universal Higson-Roe six-term exact sequence for the transformation g
Externí odkaz:
http://arxiv.org/abs/2411.00182
Autor:
Wiemeler, Michael
We prove vanishing results for Witten genera of string generalized complete intersections in homogeneous $\text{Spin}^c$-manifolds and in other $\text{Spin}^c$-manifolds with Lie group actions. By applying these results to Fano manifolds with second
Externí odkaz:
http://arxiv.org/abs/2410.21412
Autor:
Sire, Yannick, Xu, Tian
We introduce a new parabolic flow deforming any Riemannian metric on a spin manifold by following a constrained gradient flow of the total scalar curvature. This flow is built out of the well-known Dirac-Einstein functional. We prove local well-posed
Externí odkaz:
http://arxiv.org/abs/2409.12430
Autor:
Chai, Xiaoxiang, Wan, Xueyuan
Using spinors, we show a dihedral type rigidity for polyhedral initial data sets. This rigidity connects spacetime positive mass theorem, dihedral rigidity and capillary marginally trapped surfaces. Our method is to extend the rigidity analysis of sp
Externí odkaz:
http://arxiv.org/abs/2408.13801
Autor:
Baer, Christian
For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical radius is proved. When combined with known lower Dirac eigenvalue estimates, this has a number of geometr
Externí odkaz:
http://arxiv.org/abs/2407.21704
Autor:
Bei, Francesco, Pipoli, Giuseppe
Let $f:N\rightarrow (M,g)$ be an oriented (or spin), complete, stable, minimal, immersed hypersurface. In this paper we establish various vanishing theorems for the space of $L^2$-harmonic forms and spinors (in the spin case) under suitable positive
Externí odkaz:
http://arxiv.org/abs/2407.18836