134 research outputs found
Canonical connection on a class of Riemannian almost product manifolds
The canonical connection on a Riemannian almost product manifold is an
analogue to the Hermitian connection on an almost Hermitian manifold. In this
paper we consider the canonical connection on a class of Riemannian almost
product manifolds with non-integrable almost product structure. We construct
and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012
Natural Connection with Totally Skew-Symmetric Torsion on Riemannian Almost Product Manifolds
On a Riemannian almost product manifold we consider a linear
connection preserving the almost product structure and the Riemannian
metric and having a totally skew-symmetric torsion. We determine the class
of the manifolds admitting such a connection and prove that this
connection is unique in terms of the covariant derivative of with respect
to the Levi-Civita connection. We find a necessary and sufficient condition the
curvature tensor of the considered connection to have similar properties like
the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the
case when the torsion of the connection is parallel. We consider this
connection on a Riemannian almost product manifold constructed by a
Lie group .Comment: 14 pages, a revised edition, an example is adde
Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures
The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are
introduced as Kaehler manifolds with complex distribution of codimension two,
whose holomorphic sectional curvature only depends on the corresponding point
and the geometric angle, associated with the section. A curvature identity
characterizing such manifolds is found. The biconformal group of
transformations whose elements transform Kaehler metrics into Kaehler ones is
introduced and biconformal tensor invariants are obtained. This makes it
possible to classify the manifolds under consideration locally. The class of
locally biconformal flat Kaehler metrics is shown to be exactly the class of
Kaehler metrics whose potential function is only a function of the distance
from the origin in complex Euclidean space. Finally we show that any rotational
even dimensional hypersurface carries locally a natural Kaehler structure,
which is of quasi-constant holomorphic sectional curvatures.Comment: 36 page
The Hubble Constant from the Gravitational Lens B1608+656
We present a refined gravitational lens model of the four-image lens system
B1608+656 based on new and improved observational constraints: (i) the three
independent time-delays and flux-ratios from VLA observations, (ii) the
radio-image positions from VLBA observations, (iii) the shape of the
deconvolved Einstein Ring from optical and infrared HST images, (iv) the
extinction-corrected lens-galaxy centroids and structural parameters, and (v) a
stellar velocity dispersion, sigma_ap=247+-35 km/s, of the primary lens galaxy
(G1), obtained from an echelle spectrum taken with the Keck--II telescope. The
lens mass model consists of two elliptical mass distributions with power-law
density profiles and an external shear, totaling 22 free parameters, including
the density slopes which are the key parameters to determine the value of H_0
from lens time delays. This has required the development of a new lens code
that is highly optimized for speed. The minimum-chi^2 model reproduces all
observations very well, including the stellar velocity dispersion and the shape
of the Einstein Ring. A combined gravitational-lens and stellar dynamical
analysis leads to a value of the Hubble Constant of H_0=75(+7/-6) km/s/Mpc (68
percent CL; Omega_m=0.3, Omega_Lambda=0.7. The non-linear error analysis
includes correlations between all free parameters, in particular the density
slopes of G1 and G2, yielding an accurate determination of the random error on
H_0. The lens galaxy G1 is ~5 times more massive than the secondary lens galaxy
(G2), and has a mass density slope of gamma_G1=2.03(+0.14/-0.14) +- 0.03 (68
percent CL) for rho~r^-gamma', very close to isothermal (gamma'=2). (Abridged)Comment: 17 pages, 6 figures, 5 tables; revised version with correct fig.6 and
clarified text based on referee report; conclusions unchange
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