5 papers
The Bonnet theorem for statistical manifolds
Taiji Marugame
We prove the Bonnet theorem for statistical manifolds, which states that if a statistical manifold admits tensors satisfying the Gauss--Codazzi--Ricci equations, then it is locally…
Global secondary CR invariants in dimension five
Taiji Marugame
A global secondary CR invariant is defined as the integral of a pseudo-hermitian invariant which is independent of a choice of pseudo-Einstein contact form. We prove that any globa…
Renormalized characteristic forms of the Cheng--Yau metric and global CR invariants
Taiji Marugame
For each invariant polynomial , we construct a global CR invariant via the renormalized characteristic form of the Cheng--Yau metric on a strictly pseudoconvex domain. When the…
Chains in CR geometry as geodesics of a Kropina metric
Jih-Hsin Cheng, Taiji Marugame, Vladimir S. Matveev +1
With the help of a generalization of the Fermat principle in general relativity, we show that chains in CR geometry are geodesics of a certain Kropina metric constructed from the C…
Self-dual Einstein ACH metrics and CR GJMS operators in dimension three
Taiji Marugame
By refining Matsumoto's construction of Einstein ACH metrics, we construct a one parameter family of ACH metrics which solve the Einstein equation to infinite order and have a give…