56,597 research outputs found
Biharmonic hypersurfaces in Riemannian manifolds
We study biharmonic hypersurfaces in a generic Riemannian manifold. We first
derive an invariant equation for such hypersurfaces generalizing the biharmonic
hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH},
\cite{CMO1}, \cite{CMO2}. We then apply the equation to show that the
generalized
Chen's conjecture is true for totally umbilical biharmonic hypersurfaces in
an Einstein space, and construct a (2-parameter) family of conformally flat
metrics and a (4-parameter) family of multiply warped product metrics each of
which turns the foliation of an upper-half space of \mathhbb{R}^m by parallel
hyperplanes into a foliation with each leave a proper biharmonic hypersurface.
We also characterize proper biharmonic vertical cylinders in and .Comment: 16 pages with a correction to Theorem 3.
Multi-Photon Interference and Temporal Distinguishability of Photons
A number of recent interference experiments involving multiple photons are
reviewed. These experiments include generalized photon bunching effects,
generalized Hong-Ou-Mandel interference effects and multi-photon interferometry
for demonstrations of multi-photon de Broglie wavelength. The multi-photon
states used in these experiments are from two pairs of photons in parametric
down-conversion. We find that the size of the interference effect in these
experiments, characterized by the visibility of interference pattern, is
governed by the degree of distinguishability among different pairs of photons.
Based on this discovery, we generalize the concept of multi-photon temporal
distinguishability and relate it to a number of multi-photon interference
effects. Finally, we make an attempt to interpret the coherence theory by the
multi-photon interference via the concept of temporal distinguishability of
photons.Comment: fixed figures 4,5,
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