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111 papers · 1 filter
A note On the existence of solutions to Hitchin's self-duality equations
Yu Feng, Shuo Wang, Bin Xu
In 1987, Hitchin introduced the self-duality equations on rank-2 complex vector bundles over compact Riemann surfaces with genus greater than one as a reduction of the Yang-Mills e…
Orthogonal almost complex structure and its Nijenhuis tensor
Zizhou Tang, Wenjiao Yan
In this paper, we demonstrate that on an almost Hermitian manifold , a 2-form , the pulling back of the Kähler form on the twistor bundle over $M^{2n…
Machine learning Sasakian and topology on contact Calabi-Yau -manifolds
Daattavya Aggarwal, Yang-Hui He, Elli Heyes +3
We propose a machine learning approach to study topological quantities related to the Sasakian and -geometries of contact Calabi-Yau -manifolds. Specifically, we compute da…
Harmonic metrics of generically regular semisimple Higgs bundles on non-compact Riemann surfaces
Qiongling Li, Takuro Mochizuki
We prove that a generically regular semisimple Higgs bundle equipped with a non-degenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the…
Asymptotic Spectral Flow
Xianzhe Dai, Yihan Li
In this paper we study the asymptotic behavior of the spectral flow of a one-parameter family of Dirac operators acting on the spinor bunldle twisted by a vector bund…
Isoparametric hypersurfaces and complex structures
Zizhou Tang, Wenjiao Yan
The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres. As a consequence, complex structures on $…