Let M be an n-dimensional projective algebraic manifold in certain projective space CP . The hyperplane line bundle of CP restricts to an ample line bundle L on M , which is called a polarization of M . A Kähler metric g is called a polarized metric, if the corresponding Kähler form represents the first Chern class c1(L) of L in H (M,Z). Given any polarized Kähler metric g, there is a Hermitian...

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...

Any three-dimensional metric g may be locally obtained from a constant curvature metric, h , by a deformation like

In this article we show that any finite cover of the moduli space of closed Riemann surfaces of g genus with g > 2 does not admit any complete finite-volume Hermitian metric of non-negative scalar curvature. Moreover, we also show that the total mass of the scalar curvature of any almost Hermitian metric, which is equivalent to the Teichmüller metric, on any finite cover of the moduli space is ...

Azam, A Fisfer, B, Khan, M: Common fixed point theorems in complex valued metric Spaces. Number. Funct. Anal. Optim. . 32(3), 243-253 (2011). B. C. Dhage, Generalized metric spaces and mappings with fixed point, Bull. Calcutt Math. Soc. 84 (1992), 329-336. B. C. Dhage, " On generalized metric spaces and topological structure. II," Pure and applied Mathematika Sciences, Vol. 40, no. 1-...

We study the topological-antitopological fusion equations for supersymmetric σ-models on Grassmannian manifolds G(k,N). We find a basis in which the metric becomes diagonal and the tt equations become tractable. The solution for the metric of G(k,N) can then be described in terms of the metric for the CPmodels. The IR expansion helps clarify the picture of the vacua and gives the soliton number...

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This paper introduces the concept of Fg-metric Space. We generalize G-metric space. Some supporting examples are given.

Let G be a connected graph. A vertex w strongly resolves a pair u, v of vertices of G if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set W of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of W . The smallest cardinality of a strong resolving set for G is called the strong metric dime...

We extend the Khinchin–Kahane inequality to an arbitrary abelian metric group G . In the special case where G is normed, we prove a refinement which is sharp and which extends the sharp version for Banach spaces. We also provide an alternate proof for normed metric groups as a consequence of a general “transfer principle”. This transfer principle has immediate applications to stochastic inequal...