Geometric graph manifolds with non‐negative scalar curvature

Autor: Wolfgang Ziller, Luis A. Florit

Publikováno v: Journal of the London Mathematical Society. 104:1475-1490

We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if $n>3$, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the 3-dimensional case

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b48d09e8b0bf8360e9d2542649b27a7
https://doi.org/10.1112/jlms.12466

Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$

Autor: Wolfgang Ziller, Vladimir S. Matveev, Patrick Foulon, Sergei Ivanov, Robert L. Bryant

Publikováno v: J. Differential Geom. 117, no. 1 (2021), 1-22
Journal of Differential Geometry
Journal of Differential Geometry, In press, 117 (1), pp.1-22. ⟨10.4310/jdg/1609902015⟩
Journal of Differential Geometry, International Press, In press, 117 (1), pp.1-22. ⟨10.4310/jdg/1609902015⟩
Journal of Differential Geometry, International Press, In press

International audience; We study non-reversible Finsler metrics with constant flag curvature 1 on S 2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1-parameter family. In particular

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3c3cba72e2e57542e32849b936c8c39
https://projecteuclid.org/euclid.jdg/1609902015

Smoothness conditions in cohomogeneity one manifolds

Autor: Luigi Verdiani, Wolfgang Ziller

We present an efficient method for determining the conditions that a metric on a cohomogeneity one manifold, defined in terms of functions on the regular part, needs to satisfy in order to extend smoothly to the singular orbit.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6a7828e630a3e6b52c43a553fae5829
http://hdl.handle.net/2158/1213410

The prescribed Ricci curvature problem for naturally reductive metrics on compact Lie groups

Autor: Romina M. Arroyo, Artem Pulemotov, Wolfgang Ziller

Publikováno v: Differential Geometry and its Applications. 78:101794

We study the problem of prescribing the Ricci curvature in the class of naturally reductive metrics on a compact Lie group. We derive necessary as well as sufficient conditions for the solvability of the equations and provide a series of examples.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::cb236c9865f3b0f81ea4076e04adaa25
https://doi.org/10.1016/j.difgeo.2021.101794

Reversible homogeneous Finsler metrics with positive flag curvature

Autor: Ming Xu, Wolfgang Ziller

Publikováno v: Forum Mathematicum. 29:1213-1226

In this work, we continue with the classification for positively curve homogeneous Finsler spaces ( G / H , F ) {(G/H,F)} . With the assumption that the homogeneous space G / H {G/H} is odd dimensional and the positively curved metric F is reversible

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4aff9fb050c13f643412b181fa3f481
https://doi.org/10.1515/forum-2016-0173