Juan A. Aledo
Curvature properties of compact spacelike hypersurvaces in de Sitter space
A sufficient condition for a compact
spacelike hypersurface in de Sitter space to be spherical in terms of
a lower bound for the square of its mean curvature is presented.
Our result will be
a consequence of the maximum principle for the Laplacian operator. We
also derive some other applications and consequences of our main
result. In particular, we establish another sufficient condition for a
compact spacelike hypersurface in de Sitter space to be spherical in
terms of a pinching condition for its scalar curvature, as well as in
terms of the Ricci curvature and in terms of the higher order mean
curvatures.
Luis J. Alias
Maximal surfaces in the Lorentz-Minkowski space and
Calabi-Bernstein's theorem
A maximal surface in the Lorentz-Minkowski space is a spacelike surface
with zero mean curvature everywhere. Calabi-Bernstein's theorem states that
the only entire maximal
graphs in the
Lorentz-Minkwoski space are the spacelike planes. In
this talk we
will present a new approach to Calabi-Bernstein's theorem which is based on
a local
integral inequality for the Gaussian curvature of a maximal surface,
involving the
local geometry of the surface and its hyperbolic image. As an application
of this, we
will provide a new proof of Calabi-Bernstein's theorem.
Mitsunori Ara
The stability of F-harmonic maps
The notion of
F-harmonic maps (which unifies p-harmonic and exponentially harmonic
maps) is defined, and the stability of F-harmonic
maps reported. In
particular, we consider the following problem:
Find compact Riemannian manifolds which are neither the domain nor target
of any nonconstant stable F-harmonic map.
We describe the properties of such a manifold. Lastly, we give a
complete list of all compact irreducible symmetric spaces for which the
identity map is unstable as an F-harmonic map.
Kadri Arslan
On contact metric manifolds
In this study we consider pseudosymmetric and pseudo Ricci
symmetric manifolds which were introduced by M. C. Chaki.
We show that, if M is a pseudosymmetric contact metric manifold of
Chaki type with z belonging to (k,m)- nullity distribution then M is
non-Sasakian or isometric to the product E^{n+1}x S^n(4), or has
vanishing scalar curvature. We also show that, if M is a pseudo Ricci
symmetric contact metric manifold of Chaki type with z belonging to
(k,m)-nullity distribution then M has vanishing scalar curvature.
Livia Bejan
Pluriharmonic maps from the manifolds endowed with f-structures
The notion of pluriharmonicity is extended from the Hermitian manifolds to
the
manifolds endowed with a structure of K.Yano type. Some conditions under
which
a pluriharmonic map is f-holomorphic (or f-antiholomorphic) are given.
Some special submanifolds are studied in this context.
Mohamed Belkhelfa
Sasakian manifolds and pseudosymmetry
It was proved by Deprez , Deszcz and Verstraelen that there are non
semi symmetric
pseudosymmetric Kahlerian manifolds, a similar theorem was obtained for
Ricci
pseudosymmetry by Olszak. However, the pseudosymmetry condition is non
essential
in Kahlerian manifolds. He introduced the following curvature condition
of
pseudosymmetry type on Kahlerian manifolds $(M,g,J)$:
$$\bar{R}(X,Y)\cdot R= L(X\wedge_{g}Y+JX\wedge_{g}JY-2g(JX,JY)\cdot
R,$$
where $L$ is a certain function on $M$; $g$, $J$,$R$ denote the
Kahlerian
metric, the comlex structure, the Riemannian curvature tensor and
$\bar{R}(X,Y)=X\wedge_{g}Y+JX\wedge_{g}JY-2g(JX,JY).$ There are many
examples of
non semisymmetric Bochner flat manifolds satisfying the above
condition.
We investigate the pseudosymmetry of Sasakian manifolds.
Emma Carberry.
Harmonic tori: an algebraic perspective.
I will explain the method by which Hitchin reduced the
study of harmonic tori in the 3-sphere to a problem in the theory of
algebraic curves, and discuss approaches for further study.
Ryszard Deszcz
Examples of non-semisymmetric Ricci-semisymmetric hypersurfaces
We will present examples of non-semisymmetric Ricci-semisymmetric
hypersurfaces of semi-Euclidean spaces.
Sorin Dragomir
Harmonic maps in CR geometry
Ugur Dursun
Minimal Lorentzian Hypersurfaces Foliated by Geodesics of
4-dimensional Lorentzian Space Forms.
Let M be a connected space-like surface in a 4-dimensional space
form N. We define a Lorentzian hypersurface P which is the image
of a subbundle of the normal bundle of M spanned by
a time-like unit normal vector field in
N under the normal exponential mapping of M in N.
We show that
P is minimal in N under some conditions on the components of the
normal
connection form. We also build up some examples.
Atsushi Fujioka
On some generalizations of constant mean curvature surfaces
We introduce some classes of surfaces in space
forms
as a natural generalization of constant mean curvature surfaces and
consider basis properties for them.
Malgorzata Glogowska
On a class of semisymmetric manifolds
We will present curvature properties of semi-Riemannian
manifolds (M,g), n>3, whose Weyl tensor is expressed
by the square, in the sense of the product of Kulkarni-Nomizu,
of the tensor S - (\kappa/(n-1))g.
Claudio Gorodski
The converse to a theorem by Bott and Samelson
We develop a technique based on methods of representation theory of
compact Lie groups and the osculating spaces of orbits that enable us
to study several geometrically interesting classes of manifolds, with
some important applications including the converse to a theorem of
Bott and Samelson and new results about taut manifolds, as well as
simpler proofs of other classification results.
Martin Kilian
New Constant Mean Curvature Cylinders
Using the DPW method, I shall show how
to solve period closing problems to obtain new examples of CMC
cylinders of non-finite type.
Dorota Kowalczyk
Curvature properties of some spacetimes
We will present curvature properties of the Schwarzschild-type
spacetimes.
Catherine McCune
Rational Minimal Surfaces
A special class of minimal surfaces of genus zero with finite total
curvature, with Enneper type ends, and without umbilics will be
described. The UP-iteration - a combination of Moebius
transformations and Christoffel transformations - for the Gauss maps
of these surfaces will be introduced. It will be used to produce
infinitely many families of these surfaces, the proof relies on
properties of the Schwarzian derivative.
Ian McIntosh
Algebraic harmonic tori
I will describe a way of looking at harmonic tori in
some symmetric spaces which highlights the algebraic properties and
raise a few questions concerning the existence of purely algebraic
examples.
Hiroshi Matsuzoe
Semi-Weyl structures and conformal-projective
transformations in affine differential geometry.
We introduce a semi-Weyl structure
in order to construct a unified theory for
Weyl structure and statistical structure.
We also introduce conformal-projective transformations.
We then give a necessary and sufficient condition for a
semi-Weyl manifold to be a space of constant curvature.
Xiaohuan Mo
Harmonic maps from Finsler spaces
We introduce the energy, the Euler-Lagrange operator and the
stress
energy tensor for a smooth map $\phi$ from a Finisher manifold to a
Romanian manifold. We show that $\phi$ is an extremal of the energy
functional if and only if $\phi$ satisfies the corresponding
Euler-Lagrange equation. We also characterize weak Landsberg manifolds
in terms of harmonicity and horizontal conservativity. Using the
representation of tensor fields in terms of geodesic coefficients, we
construct new examples of harmonic maps from Berwald spaces which are
neither Riemannian nor Minkowskian.
Stefano Montaldo
Biharmonic curves on a
Surface
Zerrin Senturk
Generalized Einstein metric conditions
Einstein Manifolds form a natural subclass of various classes of
Semi-Riemannian manifolds determined by a curvature condition imposed
on their Ricci tensor. Certain pseudosymmetry type curvature
conditions give rise to new examples of generalized Einstein metric
conditions.
An extension of the class of Einstein manifolds form quasi-Einstein
manifolds. In this way we get other generalized Einstein metric
conditions.
After we construct examples of compact Ricci-pseudosymmetric
manifolds,
we present some results on Quasi-Einstein manifolds satisfying some
curvature conditions of pseudosymmetry type. Next we introduce four
new curvature conditions of pseudosymmetry type. We state that any
Einstein manifold satisfies these conditions.
Hiroshi Tamaru
Symmetric spaces and two-step nilpotent
Lie groups
We construct a class of two-step nilmanifolds from compact
symmetric spaces. These nilmanifolds can be investigated in
terms of the theory of symmetric spaces, similarly to the
studies on H-type groups in terms of Clifford modules.
We want to mention the following properties of our
nilmanifolds: the construction, the isometry groups,
singularity, weak symmetry, and so on.
Seiichi Udagawa
Harmonic maps of finite type into generalized flag manifolds
and twistor fibrations
I will talk about the following :
(1) An improvement of Burstall's result on harmonic
maps
of
finite type into a sphere or a complex projective space and
its
generalization;
(2) A classification of pluriharmonic maps from the n-dimensional
complex torus
into a complex projective space;
(3) A new integrable system of harmonic maps
from
compact Riemann surfaces of higher genus into a k-symmetric
space.
Marina Ville
Harmonic morphisms from 4-manifolds to surfaces.
If M and N are Riemannian manifolds, a harmonic morphism
f:M->N is a map which pulls back local harmonic
functions on N to local harmonic functions on M. If M is an
Einstein 4-manifold and N is a Riemann surface, John Wood showed
that f is holomorphic w.r.t. some integrable complex structure
defined on M away from the singular points of f. In this paper we
extend this complex structure to the whole manifold M. If M is
compact, it admits a metric which is Kaehler w.r.t this complex
structure. It follows that there are no non-constant harmonic
morphisms from S^4 or CP^2 to a Riemann surface.
The proof relies heavily on the real analyticity of the whole
situation.