284 research outputs found
Do Killing-Yano tensors form a Lie Algebra?
Killing-Yano tensors are natural generalizations of Killing vectors. We
investigate whether Killing-Yano tensors form a graded Lie algebra with respect
to the Schouten-Nijenhuis bracket. We find that this proposition does not hold
in general, but that it does hold for constant curvature spacetimes. We also
show that Minkowski and (anti)-deSitter spacetimes have the maximal number of
Killing-Yano tensors of each rank and that the algebras of these tensors under
the SN bracket are relatively simple extensions of the Poincare and (A)dS
symmetry algebras.Comment: 17 page
3-quasi-Sasakian manifolds
In the present paper we carry on a systematic study of 3-quasi-Sasakian
manifolds. In particular we prove that the three Reeb vector fields generate an
involutive distribution determining a canonical totally geodesic and Riemannian
foliation. Locally, the leaves of this foliation turn out to be Lie groups:
either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian
manifolds have a well-defined rank, obtaining a rank-based classification.
Furthermore, we prove a splitting theorem for these manifolds assuming the
integrability of one of the almost product structures. Finally, we show that
the vertical distribution is a minimum of the corrected energy.Comment: 17 pages, minor modifications, references update
Conformal Yano-Killing tensor for the Kerr metric and conserved quantities
Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed.
Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime
are obtained from the Yano--Killing tensor. The relation between spin-2 fields
and solutions to the Maxwell equations is used in the construction of a new
conserved quantity which is quadratic in terms of the Weyl tensor. The formula
obtained is similar to the functional obtained from the Bel--Robinson tensor
and is examined in Kerr spacetime. A new interpretation of the conserved
quantity obtained is proposed.Comment: 29 page
A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
We discuss a deformation of Sasakian structure in the presence of totally
skew-symmetric torsion by introducing odd dimensional manifolds whose metric
cones are K\"ahler with torsion. It is shown that such a geometry inherits
similar properties to those of Sasakian geometry. As an example of them, we
present an explicit expression of local metrics and see how Sasakian structure
is deformed by the presence of torsion. We also demonstrate that our example of
the metrics admits the existence of hidden symmetries described by non-trivial
odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using
these metrics as an {\it ansatz}, we construct exact solutions in five
dimensional minimal (un-)gauged supergravity and eleven dimensional
supergravity. Finally, we discuss the global structures of the solutions and
obtain regular metrics on compact manifolds in five dimensions, which give
natural generalizations of Sasaki--Einstein manifolds and
. We also discuss regular metrics on non-compact manifolds in eleven
dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra
Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated.
The intimate relation between Killing-Yano tensors and non-standard
supersymmetries is pointed out. In the Dirac theory on curved spaces,
Killing-Yano tensors generate Dirac type operators involved in interesting
algebraic structures as dynamical algebras or even infinite dimensional
algebras or superalgebras. The general results are applied to space-times which
appear in modern studies. One presents the infinite dimensional superalgebra of
Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be
seen as a twisted loop algebra. The existence of the conformal Killing-Yano
tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia,
August 200
Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional
spacetime with such a principal Killing-Yano tensor, we show how to generate
k=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and k
rank-2 Killing tensors, giving k constants of geodesic motion that are in
involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with
its principal Killing-Yano tensor (gr-qc/0610144), these constants and the
constants from the k Killing vectors give D independent constants in
involution, making the geodesic motion completely integrable (hep-th/0611083).
The constants of motion are also related to the constants recently obtained in
the separation of the Hamilton-Jacobi and Klein-Gordon equations
(hep-th/0611245).Comment: 7 page
Analysis of phenolic compounds in rhubarbs using liquid chromatography coupled with electrospray ionization mass spectrometry
Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general
rotating asymptotically de Sitter black hole with NUT parameters. It is known
that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY)
tensor as a ``hidden'' symmetry which provides the separation of variables for
the geodesic equations and Klein-Gordon equations. We present a classification
of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This
provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular,
we show that the Kerr-NUT-de Sitter spacetime is the only spacetime with a
non-degenerate CKY tensor.Comment: 24 pages, LaTeX; v2: references added, published versio
Production of benzylisoquinoline alkaloids in Saccharomyces cerevisiae
The benzylisoquinoline alkaloids (BIAs) are a diverse class of metabolites that exhibit a broad range of pharmacological activities and are synthesized through plant biosynthetic pathways comprised of complex enzyme activities and regulatory strategies. We have engineered yeast to produce the key intermediate reticuline and downstream BIA metabolites from a commercially available substrate. An enzyme tuning strategy was implemented that identified activity differences between variants from different plants and determined optimal expression levels. By synthesizing both stereoisomer forms of reticuline and integrating enzyme activities from three plant sources and humans, we demonstrated the synthesis of metabolites in the sanguinarine/berberine and morphinan branches. We also demonstrated that a human P450 enzyme exhibits a novel activity in the conversion of (R)-reticuline to the morphinan alkaloid salutaridine. Our engineered microbial hosts offer access to a rich group of BIA molecules and associated activities that will be further expanded through synthetic chemistry and biology approaches
The Prolyl Isomerase Pin1 Modulates Development of CD8+ cDC in Mice
We have identified a novel role for Pin1 as a modulator of CD8+ cDC development. Consistent with reduced numbers of CD8+ cDC in Pin1-null mice, we find that the absence of Pin1 impairs CD8+ T cell proliferation in response to infection with Listeria monocytogenes. These data suggest that, via regulation of CD8+ cDC production, Pin1 may serve as an important modulator of adaptive immunity
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