127 citations · 305 across the 22 of their papers we have counts for
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Holonomy restrictions from the curvature operator of the second kind
Jan Nienhaus, Peter Petersen, Matthias Wink +1
We show that an -dimensional Riemannian manifold with -nonnegative or -nonpositive curvature operator of the second kind has restricted holonomy or is flat. The re…
Rigidity of Homogeneous Gradient Soliton Metrics and Related Equations
Peter Petersen, William Wylie
We prove structure results for homogeneous spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function and an invariant 2-te…
Curvature-dimension bounds for Lorentzian splitting theorems
Eric Woolgar, William Wylie
We analyze Lorentzian spacetimes subject to curvature-dimension bounds using the Bakry-Émery-Ricci tensor. We extend the Hawking-Penrose type singularity theorem and the Lorentzian…
The weighted connection and sectional curvature for manifolds with density
Lee Kennard, William Wylie, Dmytro Yeroshkin
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last t…
On the geometry of Riemannian manifolds with density
William Wylie, Dmytro Yeroshkin
We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplaci…
Cosmological singularity theorems and splitting theorems for N-Bakry-Emery spacetimes
Eric Woolgar, William Wylie
We study Lorentzian manifolds with a weight function such that the -Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theori…