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Counting orbits of certain infinitely generated non-sharp discontinuous groups for the anti-de Sitter space
Inspired by an example of Guéritaud and Kassel (Geom Topol 21(2):693–840, 2017), we construct a family of infinitely generated discontinuous groups
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Anti-de Sitter Geometry and Teichmüller Theory
The aim of this chapter is to provide an introduction to Anti-de Sitter geometry, with special emphasis on dimension three and on the relations with...
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Chern–Simons theory and cohomological invariants of representation varieties
We prove a general local rigidity theorem for pull-backs of homogeneous forms on reductive symmetric spaces under representations of discrete groups....
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The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces
The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian...
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Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration
We derive an integral representation for the subelliptic heat kernel of the complex anti-de Sitter fibration. Our proof is different from the one...
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Yamabe and Quasi-Yamabe Solitons on Hypersurfaces in the Complex Hyperbolic Space
In this paper, we give a complete classification of Yamabe solitons and gradient Yamabe solitons on real hypersurfaces in the complex hyperbolic...
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Octonionic Brownian Windings
We define and study windings along Brownian paths on octonionic, Euclidean, projective, and hyperbolic spaces which are isometric to 8-dimensional...
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Cone 3-Manifolds
This is an overview on hyperbolic cone 3-manifolds, their deformation theory and their role in Thurston’s orbifold theorem. We also describe the...
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Slant Surfaces in Kaehler Manifolds
The theory of submanifolds of a Kaehler manifold is one of the most interesting topics in differential geometry. According to the behavior of the...
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Conformally flat, minimal, Lagrangian submanifolds in complex space forms
We investigate n -dimensional ( n ⩾ 4), conformally flat, minimal, Lagrangian submanifolds of the n -dimensional complex space form in terms of the...
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On character varieties of singular manifolds
In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic...
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Quasi-Fuchsian Co-Minkowski Manifolds
Since the work of W.P. Thurston, some maps from Teichmüller space into itself can be described using the extrinsic geometry of surfaces in three...
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Recent Developments on Chen–Ricci Inequalities in Differential Geometry
One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main...
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Certain submanifolds of complex space forms
After recalling the geometric meaning of the commutativity of the second fundamental tensor of a real hypersurface of a complex space form and its...
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The Dirac Operator in Geometry and Physics
The theme of these notes is centered around the use of the Dirac operator in geometry and physics, with the main focus on scalar curvature, Gromov’s...
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Energy of sections of the Deligne–Hitchin twistor space
We study a natural functional on the space of holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, generalizing the...
