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Affine Hermitian-Einstein Metrics [PDF]
Asian Journal of Mathematics, 2009 We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our paper presents a parallel to Donaldson-Uhlenbeck-Yau's proof of the existence of Hermitian-Einstein metrics on K
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RC-positive metrics on rationally connected manifolds
Forum of Mathematics, Sigma, 2020 In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric $\omega $ such that $(T_X,\omega )$ is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective
Xiaokui Yang
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Finding of the Metric Operator for a Quasi-Hermitian Model
Journal of Function Spaces and Applications, 2013 We consider on an appropriate Sobolev space a non-Hermitian Hamiltonian depending on the two complex parameters α and β and having real spectrum. We derive a closed formula for a family of the metric operators, which render the Hamiltonian Hermitian ...
Ebru Ergun
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PT-symmetric non-Hermitian Hamiltonian and invariant operator in periodically driven SU(1,1) system
Results in Physics, 2022 We study in this paper the time evolution of PT-symmetric non-Hermitian Hamiltonian consisting of periodically driven SU(1,1)generators. A non-Hermitian invariant operator is adopted to solve the Schrödinger equation, since the time-dependent Hamiltonian
Yan Gu +3 more
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Balanced Hermitian metrics from SU(2)-structures [PDF]
Journal of Mathematical Physics, 2009 We study the intrinsic geometrical structure of hypersurfaces in six-manifolds carrying a balanced Hermitian SU(3)-structure, which we call balanced SU(2)-structure. We provide sufficient conditions, in terms of suitable evolution equations, which imply that a five-manifold with such structure can be isometrically embedded as a hypersurface in a ...
M. Fernandez +3 more
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Comptes Rendus. Mathématique, 2021 In this note, We show that over a compact Hermitian manifold $(X, \omega )$ whose metric satisfies $\partial \bar{\partial }\omega ^{n - 1} = \partial \bar{\partial }\omega ^{n - 2} = 0$, every pseudo-effective vector bundle with vanishing first Chern ...
Chen, Yong
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Metric operators for quasi-Hermitian Hamiltonians and symmetries of equivalent Hermitian Hamiltonians [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 6 pages, published ...
Alí Mostafazadeh
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A note about almost contact metric hypersurfaces axioms for almost Hermitian manifolds
Дифференциальная геометрия многообразий фигурFrom 1950s, it is known that an almost contact metric structure is induced on an arbitrary oriented hypersurface in an almost Hermitian manifold. In accordance with the definition, an almost Hermitian manifold satisfies the axiom of almost contact ...
A. Abu-Saleem +2 more
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Hunting for the non-Hermitian exceptional points with fidelity susceptibility
Physical Review Research, 2021 The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems over a decade, where the fidelity susceptibility density approaches +∞ in the thermodynamic limits.
Yu-Chin Tzeng +3 more
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Explicit doubly-hermitian metrics
Differential Geometry and its Applications, 1999 The author constructs examples of four-dimensional Riemannian manifolds admitting two independent compatible Hermitian structures. Here, compatible means same orientation.
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