Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Loubeau, Eric"'
This work seeks to advance the understanding of the smooth structure of the moduli space of self-dual contact instantons (SDCI) on Sasakian 7-manifolds M. A neighborhood of a smooth point of M is locally modeled on the first cohomological group of an
Externí odkaz:
http://arxiv.org/abs/2404.09634
We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold with suffic
Externí odkaz:
http://arxiv.org/abs/2211.05197
Publikováno v:
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXV (2024), 151-215
We formulate and study the isometric flow of $\mathrm{Spin}(7)$-structures on compact $8$-manifolds, as an instance of the harmonic flow of geometric structures. Starting from a general perspective, we establish Shi-type estimates and a correspondenc
Externí odkaz:
http://arxiv.org/abs/2109.06340
Publikováno v:
The Journal of Geometric Analysis 32, 240 (2022)
We describe the $10$-dimensional space of $Sp(2)$-invariant $G_2$-structures on the homogeneous $7$-sphere $S^7=Sp(2)/Sp(1)$ as $\mathbb{R}^+\times Gl^+(3,\mathbb{R})$. In those terms, we formulate a general Ansatz for $G_2$-structures, which realise
Externí odkaz:
http://arxiv.org/abs/2103.11552
Given two Riemannian manifolds $(B,g_B)$ and $(F,g_F)$, we give harmonicity conditions for vector fields on the Riemannian warped product $B\times_fF$, with $f:B \longrightarrow ]0,+\infty[$, using a characteristic variational condition. Then, we app
Externí odkaz:
http://arxiv.org/abs/2009.13296
We study properties of non-minimal biharmonic hypersurfaces of spheres. The main result is a CMC Unique Continuation Theorem for biharmonic hypersurfaces of spheres. We then deduce new rigidity theorems to support the Conjecture that biharmonic subma
Externí odkaz:
http://arxiv.org/abs/2007.06527
Akademický článek
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Akademický článek
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Autor:
Loubeau, Eric, Earp, Henrique N. Sá
Publikováno v:
Annals of Global Analysis and Geometry, 64 (4), 2023
We give a twistorial interpretation of geometric structures on a Riemannian manifold, as sections of homogeneous fibre bundles, following an original insight by Wood (2003). The natural Dirichlet energy induces an abstract harmonicity condition, whic
Externí odkaz:
http://arxiv.org/abs/1907.06072
We find some integral formulas of Simons and Bochner type and use them to study biharmonic and biconservative submanifolds in space forms. We obtain rigidity results that in the biharmonic case represent partial answers to two well-known conjectures
Externí odkaz:
http://arxiv.org/abs/1801.07879