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A Grassmann manifold handbook: basic geometry and computational aspects
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in...
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Embedding the Kepler Problem as a Surface of Revolution
Solutions of the planar Kepler problem with fixed energy h determine geodesics of the corresponding Jacobi–Maupertuis metric. This is a Riemannian...
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Spacelike Hypersurfaces in Spatially Parabolic Standard Static Spacetimes and Calabi–Bernstein-Type Problems
Complete spacelike hypersurfaces in spatially parabolic standard static spacetimes are studied. Under natural boundedness assumptions, we show how...
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Modular invariance and anomaly cancellation formulas in odd dimension II
By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on (4 r − 1)-dimensional...
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The equivariant family index theorem in odd dimensions
In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed’s odd dimensional index formula. Then we...
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A geometric introduction to the two-loop renormalization group flow
The Ricci flow has been of fundamental importance in mathematics, most famously through its use as a tool for proving the Poincaré conjecture and...
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The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen...
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Statistical structures on metric path spaces
The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear...
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A note on modular forms and generalized anomaly cancellation formulas
By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the...
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A spinorial characterization of hyperspheres
Let M be a compact orientable n -dimensional hypersurface, with nowhere vanishing mean curvature H , immersed in a Riemannian spin manifold
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Geometric aspects of the Kapustin–Witten equations
This expository paper introduces the Kapustin–Witten equations to mathematicians. We discuss the connections between the complex Yang–Mills equations...
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Volume comparison for hypersurfaces in Lorentzian manifolds and singularity theorems
We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds,...
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Symplectic half-flat solvmanifolds
We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we...
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Foliations of lightlike hypersurfaces and their physical interpretation
This paper deals with a family of lightlike (null) hypersurfaces ( H u ) of a Lorentzian manifold M such that each null normal vector ℓ of H ...
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Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case
Since the pioneering work of Canham and Helfrich, variational formulations involving curvature-dependent functionals, like the classical Willmore...
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Skew Killing spinors
We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and...
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Dirac-Lu space with pseudo-Riemannian metric of constant curvature
In this paper, we will discuss the geometries of the Dirac-Lu space whose boundary is the third conformal space N defined by Dirac and Lu. We firstly...
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Modular invariance and anomaly cancellation formulas
By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas. As an application, we derive...
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Lower bounds for the eigenvalues of the Spin c Dirac-Witten operator
In this paper, we get optimal lower bounds for the eigenvalues of the Spin c Dirac-Witten operator. These estimates are given in terms of the mean...