https://neckpinch.com/authors/shengda-hu/New arXiv papers by Shengda Hu, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2206.04566/arxiv:2206.04566Thu, 09 Jun 2022 00:00:00 GMTShengda Hu — Employing a class of generalized connections, we describe certain differential complices (tilde Ω^*_T(M), mathbbd^(T)) constructed from ∧^* T M and study some of their basic properties, where T M = T M ⊕ T^*M is the generalized tangent bundle on M. A number of classical geometric notions are extended to T M, such as the curvature tensor for a generalized connection. In particular, we describe an analogue to the Levi-Civita connection when T M is endowed with a generalized metric and a structure of exact Courant algebroid. We further describe in generalized geometry the analogues to the Chern-Weil homomorphism, a Weitzenböck identity, the Ricci flow and Ricci soliton, the Hermitian-Einstein equation and the degree of a holomorphic vector bundle. Furthermore, the Ricci flows are put into the context of geometric Lax flows, which may be of independent interest.Ricci flowRicci solitons