21 citations · 46 across the 8 of their papers we have counts for
13 papers
Ambient and Poincaré metrics for CR -manifolds associated with the self-dual Einstein ACH metric
Taiji Marugame
We construct new ambient and Poincaré metrics for the Fefferman conformal manifold over -dimensional CR manifolds, starting from the associated self-dual Einstein ACH metric. Un…
The Fefferman Metric for Twistor CR Manifolds and Conformal Geodesics in Dimension Three
Taiji Marugame
We give an explicit description of the Fefferman metric for twistor CR manifolds in terms of Riemannian structures on the base conformal 3-manifolds. As an application, we prove th…
Hyperkähler ambient metrics associated with twistor CR manifolds
Taiji Marugame
Twistor CR manifolds, introduced by LeBrun, are Lorentzian (neutral) CR 5-manifolds defined as -bundles over 3-dimensional conformal manifolds. In this paper, we embe…
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…
Some Remarks on the Total CR and -Curvatures
Taiji Marugame
We prove that the total CR -curvature vanishes for any compact strictly pseudoconvex CR manifold. We also prove the formal self-adjointness of the -operator and the CR…
GJMS operators and Q-curvature for conformal Codazzi structures
Taiji Marugame
The conformal Codazzi structure is an intrinsic geometric structure on strictly convex hypersufaces in a locally flat projective manifold. We construct the GJMS operators and the Q…
Volume renormalization for the Blaschke metric on strictly convex domains
Taiji Marugame
We consider the volume expansion of the Blaschke metric, which is a projectively invariant metric on a strictly convex domain in a locally flat projective manifold. When the bounda…
Variation of total Q-prime curvature on CR manifolds
Kengo Hirachi, Taiji Marugame, Yoshihiko Matsumoto
We derive variational formulas for the total Q-prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q-prime cur…
Renormalized Chern-Gauss-Bonnet formula for complete Kahler-Einstein metrics
Taiji Marugame
We present a renormalized Gauss-Bonnet formula for approximate Kahler-Einstein metrics on compact complex manifolds with pseudo-Einstein CR boundaries. The boundary integral is giv…