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Global structure of spectra of periodic non-Hermitian Jacobi operators

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Science China mathematics 2024年

作者： Hui Lu Jiangong You School of mathematics Nanjing Audit University chern institute of mathematics and lpmc Nankai University

We give global structure of spectra of periodic non-Hermitian Jacobi operators by the discriminant and its stationary points. We also give necessary and sufficient conditions for real spectra and single interval spectra.

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On the Generalized Geroch Conjecture for Complete Spin Manifolds

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Chinese Annals of mathematics,Series B 2022年第6期43卷 1143-1146页

作者： Xiangsheng WANG Weiping ZHANG School of mathematics Shandong UniversityJinan 250100China chern institute of mathematics&lpmc Nankai UniversityTianjin 300071China.

Let W be a closed area enlargeable manifold in the sense of Gromov-Lawson and M be a noncompact spin manifold,the authors show that the connected sum M#W admits no complete metric of positive scalar *** W=T^(n),this p... 详细信息

关键词： Positive scalar curvature Connected sum Spin manifolds

Superconnections and an intrinsic Gauss-Bonnet-chern formula for Finsler manifolds Dedicated to Professor Shiing-Shen chern and Professor Yibing Shen

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Science China mathematics 2023年第9期66卷 1903-1932页

作者： Huitao Feng Ming Li chern institute of mathematics&lpmc Nankai UniversityTianjin 300071China Mathematical Science Research Center Chongqing University of TechnologyChongqing 400054China

In this paper,we establish an intrinsic Gauss-Bonnet-chern formula for Finsler manifolds by using the Mathai-Quillen’s superconnection formalism,in which no extra vector field is ***,we prove a more general Lichnerow... 详细信息

关键词： superconnection Gauss-Bonnet-chern formula Finsler manifold transgression

ISOPARAMETRIC HYPERSURFACES AND COMPLEX STRUCTURES

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Acta Mathematica Scientia 2022年第6期42卷 2223-2229页

作者：唐梓洲彦文娇 chern institute of mathematics&lpmc Nankai UniversityTianjin 300071China School of Mathematical Sciences Laboratory of Mathematics and Complea SystemsBeijing Normal UniversityBeijing 100875China

The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit *** a consequence,complex structures on S^(1)×S^(7)×S^(6),and on S^(10)×S^(3)×S(2)w... 详细信息

关键词： almost complex structure integrable Hermitian structure isoparametric hypersurface

Maurer-Cartan characterizations and cohomologies of compatible Lie algebras

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Science China mathematics 2023年第6期66卷 1177-1198页

作者： Jiefeng Liu Yunhe Sheng Chengming Bai School of mathematics and Statistics Northeast Normal UniversityChangchun 130024China Department of mathematics Jilin UniversityChangchun 130012China chern institute of mathematics&lpmc Nankai UniversityTianjin 300071China

In this paper,we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie ***,we first introduce the notion of a bidifferential graded Lie algebra and thus give Maurer-Cartan characterizations of compatible Lie *** we introduce a cohomology theory of compatible Lie algebras and use it to classify infinitesimal deformations and abelian extensions of compatible Lie *** particular,we introduce the reduced cohomology of a compatible Lie algebra and establish the relation between the reduced cohomology of a compatible Lie algebra and the cohomology of the corresponding compatible linear Poisson structures introduced by Dubrovin and Zhang(2001)in their study of bi-Hamiltonian ***,we use the Maurer-Cartan approach to classify nonabelian extensions of compatible Lie algebras.

关键词： compatible Lie algebra Maurer-Cartan element cohomology deformation extension

Fredholm theory for pseudoholomorphic curves with brake symmetry

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Frontiers of mathematics in China 2022年第6期17卷 1201-1234页

作者： Beijia ZHOU Chaofeng ZHU chern institute of mathematics Nankai University and LPMCTianjin300071China

We study the pseudoholomorphic curves with brake symmetry in symplectization of a closed contact *** introduce the pseudoholomorphic curves with brake symmetry and the corresponding moduli *** we get the virtual dimen... 详细信息

关键词： Pseudoholomorphic curve brake symmetry moduli space virtual dimension

Chaotic Dynamics of Monotone Twist Maps

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Acta Mathematica Sinica,English Series 2022年第1期38卷 179-204页

作者： Guo Wei YU chern institute of mathematics and lpmc Nankai UniversityTianjin 300071P.R.China

For a monotone twist map,under certain non-degenerate condition,we showed the existence of infinitely many homoclinic and heteroclinic orbits between two periodic neighboring minimal orbits with the same rotation number,which indicates chaotic *** results also apply to geodesics of smooth Riemannian metrics on the two-dimension torus.

关键词： Monotone twist maps homoclinic and heteroclinic orbits topological entropy

Projection Body and Isoperimetric Inequalities for s-Concave Functions

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Chinese Annals of mathematics,Series B 2023年第3期44卷 465-480页

作者： Niufa FANG Jiazu ZHOU School of mathematics Hunan UniversityChangsha410082China chern institute of mathematics&lpmc Nankai UniversityTianjin300071China School of mathematics and Statistics Southwest UniversityChongqing400715China College of Science Wuhan University of Science and TechnologyWuhan430081China

For a positive integer s,the projection body of an s-concave function f:R^(n)→[0,+∞),a convex body in the(n+s)-dimensional Euclidean space R^(n+s),is *** inequalities for s-concave functions,such as,the functional isoperimetric inequality,the functional Petty projection inequality and the functional Loomis-Whitney inequality are obtained.

关键词： Isoperimetric inequality s-Concave functions Projection body The Petty projection inequality

A mod 2 index theorem for pin-manifolds

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Science China mathematics 2017年第9期60卷 1615-1632页

作者： ZHANG WeiPing chern institute of mathematics&lpmc Nankai UniversityTianjin 300071China

We establish a mod 2 index theorem for real vector bundles over 8k + 2 dimensional compact pin^- manifolds. The analytic index is the reduced η invariant of(twisted) Dirac operators and the topological index is defined through KO-theory. Our main result extends the mod 2 index theorem of Atiyah and Singer(1971)to non-orientable manifolds.

关键词：定理流形 PIN 拓扑指数向量丛 MOD 狄拉克 mod