scholarly journals Homotopy type of manifolds with partially horoconvex boundary

2018 ◽  
Vol 29 (11) ◽  
pp. 1850074
Author(s):  
Changwei Xiong
Keyword(s):  
Riemannian Manifold ◽  
Finite Number ◽  
Homotopy Type ◽  
Riemannian Metric ◽  
Closed Formula ◽  
Dimension Formula ◽  
Manifold With Boundary ◽  
Cw Complex ◽  
Compact Connected Manifold ◽  
Number Of Cells

Let [Formula: see text] be an [Formula: see text]-dimensional compact connected manifold with boundary, [Formula: see text] a constant and [Formula: see text] an integer. We prove that [Formula: see text] supports a Riemannian metric with the interior [Formula: see text]-curvature [Formula: see text] and the boundary [Formula: see text]-curvature [Formula: see text], if and only if [Formula: see text] has the homotopy type of a CW complex with a finite number of cells with dimension [Formula: see text]. Moreover, any Riemannian manifold [Formula: see text] with sectional curvature [Formula: see text] and boundary principal curvature [Formula: see text] is diffeomorphic to the standard closed [Formula: see text]-ball.

Golden Riemannian structures on the tangent bundle with g-natural metrics

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2543-2554
Author(s):  
E. Peyghan ◽  
F. Firuzi ◽  
U.C. De
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Riemannian Metric

Starting from the g-natural Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g), we construct a family of the Golden Riemannian structures ? on the tangent bundle (TM,G). Then we investigate the integrability of such Golden Riemannian structures on the tangent bundle TM and show that there is a direct correlation between the locally decomposable property of (TM,?,G) and the locally flatness of manifold (M,g).

scholarly journals Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

1997 ◽  
Vol 20 (2) ◽  
pp. 397-402 ◽  
Author(s):  
E. M. E. Zayed
Keyword(s):  
Riemannian Manifold ◽  
Boundary Conditions ◽  
Finite Number ◽  
Spectral Function ◽  
Compact Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Smooth Functions ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The spectral functionΘ(t)=∑i=1∞exp(−tλj), where{λj}j=1∞are the eigenvalues of the negative Laplace-Beltrami operator−Δ, is studied for a compact Riemannian manifoldΩof dimension “k” with a smooth boundary∂Ω, where a finite number of piecewise impedance boundary conditions(∂∂ni+γi)u=0on the parts∂Ωi(i=1,…,m)of the boundary∂Ωcan be considered, such that∂Ω=∪i=1m∂Ωi, andγi(i=1,…,m)are assumed to be smooth functions which are not strictly positive.

MAGNETIZATION OF THE PURE STATES IN THE p-SPIN INTERACTION MODEL

2004 ◽  
Vol 18 (04n05) ◽  
pp. 773-784
Author(s):  
M. TALAGRAND
Keyword(s):  
Low Temperature ◽  
Finite Number ◽  
Interaction Model ◽  
Spin Interaction ◽  
Rigorous Proof ◽  
Pure States ◽  
Number Of Cells

We study the magnetization of the pure states in (a suitable version of) the p-spin interaction model at low temperature. We give a rigorous proof of the phenomenon, discovered in 1 that (very roughly speaking), at a given level of accuracy, the set of sites decomposes in a finite number of cells on which the magnetization of any different pure states are uncorrelated.

ON FINSLER MANIFOLDS WHOSE TANGENT BUNDLE HAS THE g-NATURAL METRIC

2011 ◽  
Vol 08 (07) ◽  
pp. 1593-1610 ◽  
Author(s):  
ESMAEIL PEYGHAN ◽  
AKBAR TAYEBI
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Positive Constant ◽  
Tangent Bundle ◽  
Contact Structure ◽  
Jacobi Operator ◽  
Riemannian Metric ◽  
Finsler Manifolds ◽  
Almost Contact Structure ◽  
Flat Riemannian Manifold

In this paper, we introduce a Riemannian metric [Formula: see text] and a family of framed f-structures on the slit tangent bundle [Formula: see text] of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if [Formula: see text], (ii) the Jacobi operator [Formula: see text] is zero or commuting if and only if (M, F) have the zero flag curvature.

scholarly journals The super-Sasaki metric on the antitangent bundle

2020 ◽  
Vol 17 (08) ◽  
pp. 2050122
Author(s):  
Andrew James Bruce
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Symplectic Form ◽  
Riemannian Metric ◽  
Riemannian Structure ◽  
Sasaki Metric

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalization of Sasaki’s construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

Finiteness conditions for CW complexes. Il

1966 ◽  
Vol 295 (1441) ◽  
pp. 129-139 ◽  
Keyword(s):  
Topological Space ◽  
Finite Number ◽  
Simple Form ◽  
Finite Dimension ◽  
Homotopy Equivalent ◽  
Finite Complex ◽  
Finiteness Conditions ◽  
Cw Complexes ◽  
Number Of Cells

A CW complex is a topological space which is built up in an inductive way by a process of attaching cells. Spaces homotopy equivalent to CW complexes play a fundamental role in topology. In the previous paper with the same title we gave criteria (in terms of more-or-less standard invariants of the space) for a CW complex to be homotopy equivalent to one of finite dimension, or to one with a finite number of cells in each dimension, or to a finite complex. This paper contains some simplification of these results. In addition, algebraic machinery is developed which provides a rough classification of CW complexes homotopy equivalent to a given one (the existence clause of the classification is the interesting one). The results would take a particularly simple form if a certain (rather implausible) conjecture could be established.

scholarly journals Hurewicz fibrations, almost submetries and critical points of smooth maps

2017 ◽  
Vol 29 (4) ◽  
Author(s):  
Sergio Luigi Cacciatori ◽  
Stefano Pigola
Keyword(s):  
Homotopy Type ◽  
Riemannian Manifolds ◽  
Critical Points ◽  
Smooth Maps ◽  
Metric Properties ◽  
Cw Complex

AbstractWe prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric properties of maps between compact Riemannian manifolds under curvature restrictions.

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