Explicit doubly-hermitian metrics

Affine Hermitian-einstein Metrics

Here c1(E, h) is the first Chern form of E with respect to a Hermitian metric h. The famous theorem of Donaldson [7, 8] (for algebraic manifolds only) and Uhlenbeck-Yau [24, 25] says that an irreducible vector bundle E → N is ω-stable if and only if it admits a HermitianEinstein metric (i.e. a metric whose curvature, when the 2-form part is contracted with the metric on N , is a constant times ...

Explicit Self - Dual Metrics On

We display explicit half-conformally-flat metrics on the connected sum of any number of copies of the complex projective plane. These metrics are obtained from magnetic monopoles in hyperbolic 3-space by an analogue of the Gibbons-Hawking ansatz, and are conformal compactifications of asymptotically-flat, scalar-flat Kahler metrics on «-fold blow-ups of C . The corresponding twistor spaces are ...

U ( p + 1 ) - invariant Hermitian metrics with Hermitian tensor Ricci on the manifold

Explicit Realization of Pseudo-Hermitian and Quasi-Hermitian Quantum Mechanics for Two-Level Systems

We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η+, and η+-pseudo-Hermitian operators acting in C 2. The latter represent the physical observables of a model whose Hamiltonian and Hilbert space are respectively H and C2 endowed with the inner product defined by η+. Our calculations allows for a direct demonstration of the fact...

A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the locally conformally equivalent manifolds to the hyper-Kähler manifolds of the investigated type and the case when the torsion of D is D-parallel. Curvature pro...