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pro vyhledávání: '"Richardson, Ken"'
A Riemannian metric on a closed manifold is said to be geometrically formal if the wedge product of any two harmonic forms is harmonic; equivalently, the interior product of any two harmonic forms is harmonic. Given a Riemannian foliation on a closed
Externí odkaz:
http://arxiv.org/abs/2405.10867
Autor:
Brüning, Jochen, Richardson, Ken
In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and the equivar
Externí odkaz:
http://arxiv.org/abs/1908.05165
Autor:
Habib, Georges, Richardson, Ken
Given a smooth foliation on a closed manifold, basic forms are differential forms that can be expressed locally in terms of the transverse variables. The space of basic forms yields a differential complex, because the exterior derivative fixes this s
Externí odkaz:
http://arxiv.org/abs/1906.03746
Autor:
Jung, Seoung Dal, Richardson, Ken
Publikováno v:
Doc. Math. 24 (2019), 995-1031
We study properties of the mean curvature one-form and its holomorphic and antiholomorphic cousins on a transverse K\"ahler foliation. If the mean curvature of the foliation is automorphic, then there are some restrictions on basic cohomology similar
Externí odkaz:
http://arxiv.org/abs/1808.10289
Autor:
Jung, Seoung Dal, Richardson, Ken
Publikováno v:
J. Topol. Anal. 13 (2021), no. 3, 673-698
We study basic Dolbeault cohomology and find new Weitzenb\"ock formulas on a transversely K\"ahler foliation. We investigate conditions on mean curvature and Ricci curvature that impose restrictions on basic Dolbeault cohomology. For example, we prov
Externí odkaz:
http://arxiv.org/abs/1709.05469
Autor:
Prokhorenkov, Igor, Richardson, Ken
Publikováno v:
Ann. Global Anal. Geom. 55 (2019), no.2, 309-323
Let $M$ be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on $M$ to a small tubular neighborhood of each connected component of its singular stratum is foliated-diffeomorphic to an isometric
Externí odkaz:
http://arxiv.org/abs/1708.04334