Results 51 to 60 of about 2,719,579 (161)
Biflat F‐structures as differential bicomplexes and Gauss–Manin connections
Bulletin of the London Mathematical Society, Volume 57, Issue 3, Page 786-808, March 2025.Abstract We show that a biflat F‐structure (∇,∘,e,∇∗,∗,E)$(\nabla,\circ,e,\nabla ^*,*,E)$ on a manifold M$M$ defines a differential bicomplex (d∇,dE∘∇∗)$(d_{\nabla },d_{E\circ \nabla ^*})$ on forms with value on the tangent sheaf of the manifold. Moreover, the sequence of vector fields defined recursively by d∇X(α+1)=dE∘∇∗X(α)$d_{\nabla }X_{(\alpha +1)}
Alessandro Arsie, Paolo Lorenzoni
wiley +1 more source
Conformal de Rham decomposition of Riemannian manifolds [PDF]
arXiv, 2004 We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We also obtain other related de Rham-
arxiv
All two‐dimensional expanding Ricci solitons
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract The second author and H. Yin [Ars Inveniendi Analytica. DOI 10.15781/4x5c-9q97] have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a non‐atomic Radon measure as a volume measure. This led to the discovery of a large array of new expanding Ricci solitons.
Luke T. Peachey, Peter M. Topping
wiley +1 more source
Singular Riemannian foliations and their quadratic basic polynomials [PDF]
arXiv, 2016 We present a new link between the Invariant Theory of infinitesimal singular Riemannian foliations and Jordan algebras. This, together with an inhomogeneous version of Weyl's First Fundamental Theorems, provides a characterization of the recently discovered Clifford foliations in terms of basic polynomials.
arxiv
Willmore‐type inequality in unbounded convex sets
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract In this paper, we prove the following Willmore‐type inequality: on an unbounded closed convex set K⊂Rn+1$K\subset \mathbb {R}^{n+1}$ (n⩾2$(n\geqslant 2$), for any embedded hypersurface Σ⊂K${\Sigma }\subset K$ with boundary ∂Σ⊂∂K$\partial {\Sigma }\subset \partial K$ satisfying a certain contact angle condition, there holds 1n+1∫ΣHndA⩾AVR(K)|Bn+
Xiaohan Jia +3 more
wiley +1 more source
Higher order Lipschitz Sandwich theorems
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We investigate the consequence of two Lip(γ)${\mathrm{Lip}}(\gamma)$ functions, in the sense of Stein, being close throughout a subset of their domain. A particular consequence of our results is the following. Given K0>ε>0$K_0 > \varepsilon > 0$ and γ>η>0$\gamma > \eta > 0$, there is a constant δ=δ(γ,η,ε,K0)>0$\delta = \delta (\gamma,\eta ...
Terry Lyons, Andrew D. McLeod
wiley +1 more source
Isometries, rigidity, and universal covers [PDF]
arXiv, 2005 We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively curved, locally symmetric manifold.
arxiv
Assouad–Nagata dimension of minor‐closed metrics
Proceedings of the London Mathematical Society, Volume 130, Issue 3, March 2025.Abstract Assouad–Nagata dimension addresses both large‐ and small‐scale behaviors of metric spaces and is a refinement of Gromov's asymptotic dimension. A metric space M$M$ is a minor‐closed metric if there exists an (edge‐)weighted graph G$G$ satisfying a fixed minor‐closed property such that the underlying space of M$M$ is the vertex‐set of G$G$, and
Chun‐Hung Liu
wiley +1 more source
, 2018 A famous theorem of Weyl states that if $M$ is a compact submanifold of euclidean space, then the volumes of small tubes about $M$ are given by a polynomial in the radius $r$, with coefficients that are expressible as integrals of certain scalar ...
Fu, Joseph H. G., Wannerer, Thomas
core
Anti-invariant Riemannian maps from almost Hermitian manifolds [PDF]
arXiv, 2012 As a generalization of anti-invariant Riemannian submersions, we introduce anti-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples and investigate the geometry of foliations which are arisen from the definition of an anti-Riemannian map.
arxiv