1,741 research outputs found
Kaehler submanifolds with parallel pluri-mean curvature
We investigate the local geometry of a class of K\"ahler submanifolds which generalize surfaces of constant mean curvature. The role of
the mean curvature vector is played by the -part (i.e. the -components) of the second fundamental form , which we call the
pluri-mean curvature. We show that these K\"ahler submanifolds are
characterized by the existence of an associated family of isometric
submanifolds with rotated second fundamental form. Of particular interest is
the isotropic case where this associated family is trivial. We also investigate
the properties of the corresponding Gauss map which is pluriharmonic.Comment: Plain TeX, 21 page
The Cosmological Time Function
Let be a time oriented Lorentzian manifold and the Lorentzian
distance on . The function is the cosmological
time function of , where as usual means that is in the causal
past of . This function is called regular iff for all
and also along every past inextendible causal curve. If the
cosmological time function of a space time is regular it has
several pleasant consequences: (1) It forces to be globally hyperbolic,
(2) every point of can be connected to the initial singularity by a
rest curve (i.e., a timelike geodesic ray that maximizes the distance to the
singularity), (3) the function is a time function in the usual sense, in
particular (4) is continuous, in fact locally Lipschitz and the second
derivatives of exist almost everywhere.Comment: 19 pages, AEI preprint, latex2e with amsmath and amsth
Rigid Singularity Theorem in Globally Hyperbolic Spacetimes
We show the rigid singularity theorem, that is, a globally hyperbolic
spacetime satisfying the strong energy condition and containing past trapped
sets, either is timelike geodesically incomplete or splits isometrically as
space time. This result is related to Yau's Lorentzian splitting
conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review
Surgery and the Spectrum of the Dirac Operator
We show that for generic Riemannian metrics on a simply-connected closed spin
manifold of dimension at least 5 the dimension of the space of harmonic spinors
is no larger than it must be by the index theorem. The same result holds for
periodic fundamental groups of odd order.
The proof is based on a surgery theorem for the Dirac spectrum which says
that if one performs surgery of codimension at least 3 on a closed Riemannian
spin manifold, then the Dirac spectrum changes arbitrarily little provided the
metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat
Invariant four-forms and symmetric pairs
We give criteria for real, complex and quaternionic representations to define
s-representations, focusing on exceptional Lie algebras defined by spin
representations. As applications, we obtain the classification of complex
representations whose second exterior power is irreducible or has an
irreducible summand of co-dimension one, and we give a conceptual
computation-free argument for the construction of the exceptional Lie algebras
of compact type.Comment: 16 pages [v2: references added, last section expanded
Convex Functions and Spacetime Geometry
Convexity and convex functions play an important role in theoretical physics.
To initiate a study of the possible uses of convex functions in General
Relativity, we discuss the consequences of a spacetime or an
initial data set admitting a suitably defined convex
function. We show how the existence of a convex function on a spacetime places
restrictions on the properties of the spacetime geometry.Comment: 26 pages, latex, 7 figures, improved version. some claims removed,
references adde
-minimal surface and manifold with positive -Bakry-\'{E}mery Ricci curvature
In this paper, we first prove a compactness theorem for the space of closed
embedded -minimal surfaces of fixed topology in a closed three-manifold with
positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type
lower bound of the first eigenvalue of the -Laplacian on compact manifold
with positive -Bakry-\'{E}mery Ricci curvature, and prove that the lower
bound is achieved only if the manifold is isometric to the -shpere, or the
-dimensional hemisphere. Finally, for compact manifold with positive
-Bakry-\'{E}mery Ricci curvature and -mean convex boundary, we prove an
upper bound for the distance function to the boundary, and the upper bound is
achieved if only if the manifold is isometric to an Euclidean ball.Comment: 15 page
The index of symmetry of compact naturally reductive spaces
We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold.submittedVersionFil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Tamuru, Hiroshi. Universidad de Hiroshima. Escuela de Ciencias. Departamento de Matemática; Japón.Matemática Pur
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit
Measurement of the branching ratios of the Z0 into heavy quarks
We measure the hadronic branching ratios of the Z0 boson into heavy quarks:
Rb=Gamma(Z0->bb)/Gamma(Z0->hadrons) and Rc=Gamma(Z0->cc/Gamma(Z0->hadrons)
using a multi-tag technique. The measurement was performed using about 400,000
hadronic Z0 events recorded in the SLD experiment at SLAC between 1996 and
1998. The small and stable SLC beam spot and the CCD-based vertex detector were
used to reconstruct bottom and charm hadron decay vertices with high efficiency
and purity, which enables us to measure most efficiencies from data. We obtain,
Rb=0.21604 +- 0.00098(stat.) +- 0.00073(syst.) -+ 0.00012(Rc) and, Rc= 0.1744
+- 0.0031(stat.) +- 0.0020(syst.) -+ 0.0006(Rb)Comment: 37 pages, 8 figures, to be submitted to Phys. Rev. D version 2:
changed title to ratios, used common D production fractions for Rb and Rc and
corrected Zgamma interference. Identical to PRD submissio
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