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Schubert Calculus on the Arithmetic Grassmannian
Arithmetic Grassmannian Schubert Calculus
2015/12/17
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant KÄahler metric on G(C). We study the combinatorics of
the arithmetic Schubert calculus in the Arakelov Chow ring CH(G)
HEIGHT FORMULAS FOR HOMOGENEOUS VARIETIES
HOMOGENEOUS VARIETIES Differential and integral calculus
2015/12/17
We use classicalSchubert calculus to evaluate the integral formula
of Kaiser and Kohler [KK] for the Faltings height of certain homogeneous
varieties in terms of combinatorial data, and verify thei...
DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH POTENTIALS
EQUATIONS WITH POTENTIALS DIFFERENTIAL HARNACK
2015/8/17
In this paper, we prove a differential Harnack inequality for positive
solutions of time-dependent heat equations with potentials. We also prove a gradient
estimate for the positive solution o...
Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator
Positive Curvature Operator Shrinking Ricci Solitons
2015/8/17
In this paper, we first derive several identities on a compact shrinking Ricci
soliton. We then show that a compact gradient shrinking soliton must be
Einstein, if it admits a Riemannian metri...
Multiply twisted products
Multiply twisted products index forms Killing vector fields semisymmetric metric connection Ricci tensor scalar curvature Einstein manifolds
2012/7/11
In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some ...
Geometric structures invariant to symmetries
symmetric spaces geometric structures Cartan geometries parabolic geometries homogeneous spaces extension functors
2012/7/11
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Ca...
General construction of symmetric parabolic structures
parabolic geometries contact geometries symmetric spaces extension functors
2012/7/11
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regu...
A reflexion space is generalization of a symmetric space introduced by O. Loos. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexio...
Einstein metrics in projective geometry
projective differential geometry Einstein metrics conformal differential geometry
2012/7/11
It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined...
f-Eikonal helix submanifolds and f-Eikonal helix curves
Helix submanifold Eikonal function Helix line
2012/6/15
Let M{\subset}\mathbb{R}^{n} be a Riemannian helix submanifold with respect to the unit direction d{\in}\mathbb{R}^{n} and f:M{\to}\mathbb{R} be a eikonal function. We say that M is a f-eikonal helix ...
Invariant tensors related with natural connections for a class Riemannian product manifolds
Invariant tensors natural connections class Riemannian product manifolds Differential Geometry
2012/6/29
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metr...
On a paper of Daskalopoulos and Sesum
a paper of Daskalopoulos and Sesum Differential Geometry
2012/6/29
This is an exposition of aspects of the result of Daskalopoulos and Sesum that any 2-dimensional complete noncompact ancient solution to Ricci flow with bounded positive scalar curvature and finite wi...
Local pinching estimates in 3-dim Ricci flow
Local pinching estimates 3-dim Ricci flow Differential Geometry
2012/6/30
We study curvature pinching estimates of Ricci flow on complete 3- dimensional manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on a...
An obstructions to Non-negative curvature on Bundles with Pull-back connections
nonegative sectional curvature riemannian submersions exotic spheres
2012/6/30
Motivated to study the geometry of the exotic spheres constructed in [5], we derive a necessary condition for non-negative sectional curvature in certain total spaces of Riemannian submersions with to...
Biharmonic Semi-Riemannian Submersions from 3-manifolds
Semi-Riemannian submersions 3-manifolds Differential Geometry
2012/6/30
The main interest of the present paper is to prove the dual results for semi-Riemannian submersions, i.e., a semi-Riemannian submersion from a 3-dimensional space form into a surface is biharmonic if ...