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Summary
We consider a genaralization of contact metric manifolds given by assignment of 1-formsη1, . . . ,ηsand a compatible metric gon a manifold. With some integrability conditions they are called almostS-manifolds. We give a sufficient condition regarding the curvature of an almostS-manifold to be locally isometric to a product of a Euclidean space and a sphere.
References [1] Gatoto , J. K. Singh , S. P. 2008 Projective -curvature inheritance in Finsler spaces
– 266 , 2007 . [3] A. Cayley . Question 1771 , Educ. Times , 4 : 70 – 71 , 1865 . [4] R. H. Graves . On the chord common to a parabola and the circle of curvature at any point . Ann.of Math ., 3 : 50 , 1887 . [5] J. Haag . Solution of
Treatment of water-induced curvature of the DSC heat flow rate signal
Applied to fractionated nucleation of polypropylene dispersed in water
pan measurements were subtracted from the actual measurements of the dispersions to remove the curvature of the heat flow rate signal as induced by the instrument itself. Dynamic light scattering (DLS) measurements were performed on a back
. Reventos , G . Solanes and E . Teufel . Width of convex bodies in spaces of constant curvature . Manuscripta Math ., 126 : 115 – 134 , 2008 . [21] H . Groemer . On complete convex bodies . Geom. Dedicata , 20 ( 3 ): 319 – 334 , 1986 . [22] H
In the present paper parallel submanifolds and focal points of a given submanifold with flat normal bundle are discussed provided that the ambient space has constant sectional curvature. We present shape operators of parallel submanifolds with respect to arbitrary normal vectors. Furthermore, we prove that the focal points of a submanifold with flat normal bundle form totally geodesic hypersurfaces in the normal submanifolds.
. [3] Blair , D. E. Kim , J.-S. Tripathi , M. M. 2005 On the concircular curvature tensor of a contact metric manifold J
In some previous papers the author gave an upper bound estimation for the Ricci curvature of a hypersurface in a hyperbolic space and in a sphere, see [4] and [5]. In the present paper, we give a lower bound estimation for the Ricci curvature of a compact connected embedded hypersurface in a hyperbolic space via the maximum principle given by H. Omori in [11].
The results of model calculation (direct problem solutions above model parameter space) determine an embedded continuous and differentiable surface in the Euclidean space of measurements. This multidimensional subspace contains the possible expected values of measurement vectors according to the assumed rock model as a projection of measurement points (expressing the model and real rock equivalences). The model parameters are the natural coordinates of this subspace, determining a contravariant curvilinear coordinate system (“flat world” for the inversion). The local curvature of this surface is very important factor of covariance matrices and the possible bias of estimated parameters. In this article the role of curvature is discussed and the shortage of conventional (first order) inversion is demonstrated by simple example and the possibility of bias correction.
Abstract
We considered in Example 3.1 of the paper [1] an S-structure on R2n+s . We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3s and then it is η-Einstein.
