111 citations · 187 across the 30 of their papers we have counts for
35 papers
The toric CR Yamabe problem
Eveline Legendre, Carlo Scarpa, Christina W. Tønnesen-Friedman
We study the equivariant CR Yamabe problem for a fixed-point-free torus action on a co-oriented compact contact manifold. Such examples arise naturally in the study of Sasakian man…
Robustness of CSC Sasaki existence under the join operation
Charles P. Boyer, Christina W. Tønnesen-Friedman
The main purpose of this work is to explore the existence of constant scalar curvature Sasaki metrics in the Sasaki cone of the join of two regular Sasaki manifolds, and $M_2…
Twins in K{ä}hler and Sasaki geometry
Charles P. Boyer, Hongnian Huang, Eveline Legendre +1
We introduce the notions of weighted extremal K{ä}hler twins together with the related notion of extremal Sasaki twins. In the Kähler setting this leads to a generalization of the…
Sasakian Geometry on Sphere Bundles II: Constant Scalar Curvature
Charles P. Boyer, Christina W. Tønnesen-Friedman
In a previous paper [BTF21] the authors employed the fiber join construction of Yamazaki [Yam99] together with the admissible construction of Apostolov, Calderbank, Gauduchon, and…
Existence and Non-Existence of Constant Scalar Curvature and Extremal Sasaki Metrics
Charles P. Boyer, Hongnian Huang, Eveline Legendre +1
We discuss the existence and non-existence of constant scalar curvature, as well as extremal, Sasaki metrics. We prove that the natural Sasaki-Boothby-Wang manifold over the admiss…
Constant Scalar Curvature Sasaki Metrics and Projective Bundles
Charles P. Boyer, Christina W. Tønnesen-Friedman
In this paper we consider the Boothby-Wang construction over twist 1 stage 3 Bott orbifolds given in terms of the log pair . We give explicit constant scalar…
Transverse Kähler holonomy in Sasaki Geometry and ${\oldmathcal S}$-Stability
Charles P. Boyer, Hongnian Huang, Christina V. Tønnesen-Friedman
We study the transverse Kähler holonomy groups on Sasaki manifolds $(M,{\oldmathcal S})$ and their stability properties under transverse holomorphic deformations of the characteris…
Sasakian Geometry on Sphere Bundles
Charles P. Boyer, Christina W. Tønnesen-Friedman
The purpose of this paper is to study the Sasakian geometry on odd dimensional sphere bundles over a smooth projective algebraic variety with the ultimate, but probably unachie…
Iterated Sasaki Joins and Bott Orbifolds
Charles P Boyer, Christina Tønnesen-Friedman
We present a categorical relationship between iterated Sasaki-joins and Bott orbifolds. Then we show how to construct smooth Sasaki-Einstein (SE) structures on the iterated j…
The $S^3_\bfw$ Sasaki Join Construction
Charles P. Boyer, Christina W. Tønnesen-Friedman
The main purpose of this work is to generalize the $S^3_\bfw$ Sasaki join construction $M\star_\bfl S^3_\bfw$ described in \cite{BoTo14a} when the Sasakian structure on is regu…
Some Open Problems in Sasaki Geometry
Charles P. Boyer, Hongnian Huang, Eveline Legendre +1
This paper has been submitted to the Proceedings of the Australian-German Workshop on Differential Geometry in the Large held at the mathematical research institute MATRIX in Cresw…
Sasaki-Einstein Metrics on a class of 7-Manifolds
Charles P. Boyer, Christina Tønnesen-Friedman
In this note we give an explicit construction of Sasaki-Einstein metrics on a class of simply connected 7-manifolds with the rational cohomology of the 2-fold connected sum of $S^2…
On Positivity in Sasaki Geometry
Charles P. Boyer, Christina W. Tønnesen-Friedman
It is well known that if the dimension of the Sasaki cone is greater than one, then all Sasakian structures are either positive or indefinite. We discuss the phenomenon of type cha…
Weighted extremal Kähler metrics and the Einstein-Maxwell geometry of projective bundles
Vestislav Apostolov, Gideon Maschler, Christina W. Tønnesen-Friedman
We study the existence of weighted extremal Kähler metrics in the sense of Apostolov-Calderbank-Gauduchon-Legendre and Lahdili on the total space of an admissible projective bundle…
The Kähler geometry of Bott manifolds
Charles P. Boyer, David M. J. Calderbank, Christina W. Tønnesen-Friedman
We study the Kähler geometry of stage n Bott manifolds, which can be viewed as -dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument an…
Reducibility in Sasakian Geometry
Charles P. Boyer, Hongnian Huang, Eveline Legendre +1
The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham Decomposition Theorem; however, we need a mild t…
Strongly Hermitian Einstein-Maxwell Solutions on Ruled Surfaces
Caner Koca, Christina W. Tønnesen-Friedman
This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact -manifolds that are -bundles over compact Riemann surfaces of any genus. Th…
The Einstein-Hilbert functional and the Sasaki-Futaki invariant
Charles P. Boyer, Hongnian Huang, Eveline Legendre +1
We show that the Einstein-Hilbert functional, as a functional on the space of Reeb vector fields, detects the vanishing Sasaki-Futaki invariant. In particular, this provides an obs…
On the Topology of some Sasaki-Einstein Manifolds
Charles P. Boyer, Christina W. Tønnesen-Friedman
This is a sequel to our paper arXiv:1402.2546 to appear in the Journal of Geometric Analysis in which we concentrate on developing some of the topological properties of Sasaki-Eins…
The Sasaki Join and Admissible Kähler Constructions
Charles P. Boyer, Christina W. Tønnesen-Friedman
We give a survey of our recent work describing a method which combines the Sasaki join construction with the admissible Kähler construction of to obtain new extremal and new consta…
Simply Connected Manifolds with Infinitely Many Toric Contact Structures and Constant Scalar Curvature Sasaki Metrics
Charles P. Boyer, Christina W. Tønnesen-Friedman
We study a class of simply connected manifolds in all odd dimensions greater than 3 that exhibit an infinite number of toric contact structures of Reeb type that are inequivalent a…
The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature
Charles P. Boyer, Christina W. Tønnesen-Friedman
We describe a general procedure for constructing new Sasaki metrics of constant scalar curvature from old ones. Explicitly, we begin with a regular Sasaki metric of constant scalar…
The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics
Charles P. Boyer, Christina W. Tønnesen-Friedman
By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from Kähler geometry, we recover Sasaki-Einstein metrics discovered by physicists…
Extremal Sasakian Geometry on S^3-bundles over Riemann Surfaces
Charles P. Boyer, Christina W. Tønnesen-Friedman
In this paper we study the Sasakian geometry on S^3-bundles over a Riemann surface of genus g>0 with emphasis on extremal Sasaki metrics. We prove the existence of a countably infi…