INNER STRUCTURE OF GAUSS–BONNET–CHERN THEOREM AND THE MORSE THEORY

DOI10.1142/S0217732301006004zbMath1138.37303arXivmath-ph/0212055OpenAlexW2083666476MaRDI QIDQ3508361

Peng-Ming Zhang, Yi-Shi Duan

Publication date: 27 June 2008

Published in: Modern Physics Letters A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0212055

zbMATH Keywords

Morse theoryEuler characteristicsecond fundamental tensor

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Index theory for dynamical systems, Morse-Conley indices (37B30) Sub-Riemannian geometry (53C17)

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Cites Work

• A new topological aspect in the \(\text{O}(n)\) symmetric time-dependent Ginzburg-Landau model.
• A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds
• Topological structure of Gauss–Bonnet–Chern density and its topological current
• Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem
• Supersymmetry and the Atiyah-Singer index theorem