Bismut connection on Vaisman manifolds
نویسندگان
چکیده
The holonomy of the Bismut connection on Vaisman manifolds is studied. We prove that if $$M^{2n}$$ endowed with a structure, then group contained in $${\text {U}}(n-1)$$ . compute explicitly this for particular types manifolds, namely, solvmanifolds and some classical Hopf manifolds.
منابع مشابه
Vaisman LOCALLY LAGRANGIAN SYMPLECTIC AND POISSON MANIFOLDS
We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Examples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold. Finally, we indicate the generalization of this type of symplectic structures to Poisson manifolds. The paper is the text of a lecture presented at the Conf...
متن کاملLagrange geometry on tangent manifolds by Izu Vaisman
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...
متن کاملVariations on a Theme by Bismut
Let M be a compact, connected, Riemannian manifold of dimension d, let fPt : t > 0g denote the Markov semigroups on C (M) determined by 1 2 , and let pt (x; y) denote the kernel (with respect to the Riemannian volume measure) for the operator Pt. (The existence of this kernel as a positive, smooth function is well-known, see e.g. D].) Bismut's celebrated formula, presented in B], equates r log ...
متن کاملJ an 2 00 3 Kähler - Nijenhuis Manifolds by Izu Vaisman
A Kähler-Nijenhuis manifold is a Kähler manifold M , with metric g, complex structure J and Kähler form Ω, endowed with a Nijenhuis tensor field A that is compatible with the Poisson structure defined by Ω in the sense of the theory of Poisson-Nijenhuis structures. If this happens, and if AJ = ±JA, M is foliated by im A into non degenerate Kähler-Nijenhuis submanifolds. If A is a non degenerate...
متن کاملA Natural Connection on (2, 3) Sub-riemannian Manifolds
We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2022
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-022-03108-2