Related papers: Hermitian Geometry and Complex Space-Time

Let $M$ be a closed Riemann surface, $N$ a Riemannian manifold of Hermitian non-positive curvature, $f:M\to N$ a continuous map, and $E$ the function on the Teichm\"uller space of $M$ that assigns to a complex structure on $M$ the energy of…

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…

Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…

We discuss a four-dimensional gravitational action which was obtained replacing a Randall-Sundrum type metric in the so called five-dimensional Einstein-Chern-Simons gravity action. We studied black hole solutions of the corresponding…

In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…

The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…

We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter, where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action,…

We consider the class of compact Hermitian manifolds whose Chern connection is Ambrose-Singer, namely, it has parallel torsion and curvature. We prove structure theorems for such manifolds.

In the context of the Relativistic Quantum Geometry formalism, where the cosmological constant is promoted to a dynamical variable by attributing it a geometric interpretation as a result of a flux on the boundary of a manifold and…

Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact…

Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…

Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…

A Hermitian metric $\omega$ on a complex manifold is called SKT or pluriclosed if $dd^c\omega=0$. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case…

We describe a rigidity phenomenon exhibited by the second Chern Ricci curvature of a Hermitian metric on a compact complex manifold. This yields a characterisation of second Chern Ricci-flat Hermitian metrics on several types of manifolds…

It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…

We seek for an alternative to the metric tensor $g_{\mu\nu}$ as a fundamental geometrical object in four-dimensional Riemannian manifolds. We suggest that the metric tensor $g_{\mu\nu}(P)$ at a given point $P$ of a manifold may be replaced…

Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds…

Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…

In this paper, we characterize Riemannian 4-manifold in terms of its almost Hermitian twistor spaces $(Z,g_t,\mathbb{J}_{\pm})$. Some special metric conditions (including Balanced metric condition, first Gauduchon metric condition) on…

Let group generators having finite-dimensional representation be realized as Hermitian linear differential operators without nhomogeneous terms as takes place, for example, for the SO(n) group. Then orresponding group Hamiltonians…