In this note we construct Nadel multiplier ideal sheaves using the Ricci flow on Fano manifolds. This extends a result of Phong, Šešum and Sturm. These sheaves, like their counterparts constructed by Nadel for the continuity method, can be used to obtain an existence criterion for KählerEinstein metrics. We end with a conjectural discussion on a possible extension of this result to general Kähl...

We elaborate an unified geometric approach to classical mechanics, Riemann–Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N–connection) structure. There are investigated the conditions when the fundamental geometric objects like the anchor, metric and linear connection, almost sympletic and related almost complex structures may be canonically defined b...

We obtain forms of Born-Infeld and D-brane actions that are quadratic in derivatives of X and linear in Fμν by introducing an auxiliary ‘metric’ which has both symmetric and anti-symmetric parts, generalising the simplification of the Nambu-Goto action for p-branes using a symmetric metric. The abelian gauge field appears as a Lagrange multiplier, and solving the constraint gives the dual form ...

The Hilbert energy-momentum tensor for gauge-fixed non-Abelian gauge theories, defined by the variational derivative of action with respect to space-time metric, is a under general coordinate transformations, symmetric in its indices, and BRST invariant. canonical has none these properties but Hamiltonian does correctly generate time dependence fields. It shown that $\int d^{3}x\,\sqrt{g}\;T^{0...

The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler–Lagrange equation for the energy functional is Darboux integrable. The time evolution of the Cauchy data is reduced to an ordinary differential equation of Lie type associated t...

We present generic form of the covariant nonlocal action for infrared modifications of Einstein theory recently suggested within the weak-field curvature expansion. In the lowest order it is determined by two nonlocal operators — kernels of Ricci tensor and scalar quadratic forms. In models with a low strong-coupling scale this action also incorporates the strongly coupled mode which cannot be ...

We define a class of condensed matter theories in a Newtonian framework with a Lagrange formalism so that a variant of Noether’s theorem gives the classical conservation laws: ∂tρ+ ∂i(ρv ) = 0 ∂t(ρv ) + ∂i(ρv v + p) = 0. We show that for the metric gμν defined by ĝ = g √−g = ρ ĝ = g √−g = ρv ĝ = g √−g = ρvv + p these theories are equivalent to a metric theory of gravity with Lagrangian L = LGR ...

Harmonic maps X:(S,h) --> N from a 2-manifold S with indefinite metric h to a semi-Riemannian manifold N are characterized, assuming that the induced metric I is nondegenerate. Except in one very special case, the characterizations involve a canonically determined holomorphic quadratic differential on a naturally chosen conformal structure. This is surprising because the Euler-Lagrange equation...

The study of extremal Kähler metric is initiated by the seminal works of Calabi [4], [5]. Let (M, [ω]) be a compact Kähler manifold with fixed Kähler class [ω]. For any Kähler metrics g in the fixed Kähler class [ω], the Calabi energy C(g) is defined as C(g) = M s 2 dµ, where s is the scalar curvature of g. The extremal Kähler metric is the critical point of the Calabi energy. The Euler-Lagrang...

The geometric constructions are performed on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also induced unique forms by a metric tensor (the Levi Civita and the canonical distin...