Scalar Curvature
Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I : reductivity
... For the uniqueness of constant scalar curvature K¨ahler (cscK) met- rics [9], the convexity of the so called Mabuchi’s functional turns out to be a very important ingredient. And this convexity is proved by ...
41
On Logarithmic Sobolev Inequality And A Scalar Curvature Formula For Noncommutative Tori
... the scalar curvature of the curved noncommutative 3-torus is ...the scalar curvature of the curved noncommutative 3-torus is ...the scalar curvature is computed and an explicit ...
90
Constant scalar curvature metrics on connected sums
... with scalar curvature close to ± 1 to get exactly ± 1 is different from the problem of rescaling a metric with scalar curvature close to zero to get scalar curvature of a small ...
46
Construction of constant scalar curvature Kähler cone metrics
... constant scalar curvature K¨ ahler metrics with conic singularities: existence result under small deformations of K¨ ahler classes, existence result over a Fano manifold, existence result over certain ruled ...
58
3. Three dimensional kinematic surfaces with constant scalar curvature in Lorentz{Minkowski 7-space
... the scalar curvature S of the corresponding kinematic surfaces as the quotient of hyperbolic functions {cosh mφ, sinhmφ}, and we derive the necessary and sufficient conditions for the coefficients to ...
10
Foliation by area constrained Willmore spheres near a non degenerate critical point of the scalar curvature
... mean curvature spheres near a non-degenerate critical point of the scalar ...mean curvature spheres is a second order problem since the mean curvature is a second order elliptic operator, ...
24
On area comparison and rigidity involving the scalar curvature
... the scalar curvature S of the ambient 3-manifold M ...positive scalar curvature must have genus ...Ricci curvature and the scalar curvature S of M vanish all along ...
74
Local Study of Scalar Curvature of Cyclic Surfaces Obtained by Homothetic Motion of Lorentzian Circle
... ∑ , the corresponding coefficients must vanish. From here, we will be able to describe all cyclic surfaces with constant scalar curvature obtained by the homothetic motion of the Lorentzian circle c 0 . As ...
9
Phantom and Quintessence Fields Coupled to Scalar Curvature in General f(R) Gravity Theory
... coupling scalar curvature R to matter field φ , ...to scalar field is the constant Einstein-Hilbert action, which has all invariant properties of Einstein’s ...
24
A remark on four dimensional almost Kähler Einstein manifolds with negative scalar curvature
... Sekigawa [8] proved that the conjecture is true if the scalar curvature τ of M is nonnegative. But the conjecture is still open in the case where τ is negative. Recently, applying the Seiberg-Witten theory, ...
6
On static three manifolds with positive scalar curvature
... its scalar curvature must be constant and the set of zeroes of V is a totally geodesic regular hypersurface ...Riemann curvature tensor) and has also physical interest (since n = 3 is the relevant ...
42
The CPT-RICCI Scalar Curvature Symmetry in Quantum Electro-Gravity
... On one side the quantum equation defines the evolution of the particle wave function and the associated spatial mass density distribution. On the other side, the gravity equation defines how the 4-D curvature is ...
23
Studying Scalar Curvature of Two Dimensional Kinematic Surfaces Obtained by Using Similarity Kinematic of a Deltoid
... From the view of differential geometry, deltoid is a geometric curve with non vanishing constant curvature K [2]. Similarity kinematic transformation in the n-dimensional an Euclidean space n is an affine ...
9
Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms
... Casorati curvature of a Kähler hypersurface in a complex space ...the scalar curvature is estimated from above by the normalized Casorati curvatures, while Ghişoiu obtained in [] some inequalities ...
10
1. On Kenmotsu Manifolds
... The notion of Kenmotsu manifolds was defined by K. Kenmotsu [9]. Kenmotsu proved that a locally Kenmotsu manifold is a warped product 𝐼 × 𝑓 𝑁 of an interval 𝐼 and a Kaehler manifold 𝑁 with warping function 𝑓 (𝑡) = 𝑠𝑒 𝑡 , ...
6
On the Curvature of Rotating Objects
... of curvature which differs in a remarkable way between Lorentz geometry and Euclidean ...less curvature (as measured by integrating the square of the scalar curvature) than non-rotating ...
9
Planck Constant as Adiabatic Invariant Characterized by Hubble’s and Cosmological Constants
... From astronomical observations it is well established that we live in a non-stationary Universe, in which all pa- rameters change over time. By taking into account this fact, let’s consider an isolated mechanical system ...
11
Nonlinear problem with subcritical exponent in Sobolev space
... We consider the problem of the scalar curvature on the standard four dimensional half sphere under minimal boundary conditions S:.. This article is distributed under the terms of the Cre[r] ...
11
Vol 3, No 4 (2012)
... the components of metric tensor field, the operator of covariant differentiation with respect to the Levi-Civita connection, the curvature tensor field, the Ricci tensor field and the scalar ...
6
Integrable Equations and Their Evolutions Based on Intrinsic Geometry of Riemann Spaces
... the scalar curvature based on the Riemannian metric for three- and four-dimensional Riemann spaces, a large group of nonlinear partial differential equations has been determined in both three and four ...
16