10,891 research outputs found
On compact Hermitian manifolds with flat Gauduchon connections
Given a Hermitian manifold , the Gauduchon connections are the one
parameter family of Hermitian connections joining the Chern connection and the
Bismut connection. We will call the -Gauduchon connection of , where and
are respectively the Chern and Bismut connections. It is natural to
ask when a compact Hermitian manifold could admit a flat -Gauduchon
connection. This is related to a question asked by Yau \cite{Yau}. The cases
with (a flat Chern connection) or (a flat Bismut connection) are
classified respectively by Boothby \cite{Boothby} in the 1950s or by Q. Wang
and the authors recently \cite{WYZ}. In this article, we observe that if either
or and , then is K\"ahler. We also show that, when , is always K\"ahler
unless . Note that non-K\"ahler compact Bismut flat surfaces are exactly
those isosceles Hopf surfaces by \cite{WYZ}.Comment: 9 pages. This preprint was submitted to Acta Mathematica Sinica, a
special issue dedicated to Professor Qikeng L
Proton block of proton-activated TRPV1 current.
The TRPV1 cation channel is a polymodal nociceptor that is activated by heat and ligands such as capsaicin and is highly sensitive to changes in extracellular pH. In the body core, where temperature is usually stable and capsaicin is normally absent, H(+) released in response to ischemia, tissue injury, or inflammation is the best-known endogenous TRPV1 agonist, activating the channel to mediate pain and vasodilation. Paradoxically, removal of H(+) elicits a transient increase in TRPV1 current that is much larger than the initial H(+)-activated current. We found that this prominent OFF response is caused by rapid recovery from H(+) inhibition of the excitatory current carried by H(+)-activated TRPV1 channels. H(+) inhibited current by interfering with ion permeation. The degree of inhibition is voltage and permeant ion dependent, and it can be affected but not eliminated by mutations to acidic residues within or near the ion selectivity filter. The opposing H(+)-mediated gating and permeation effects produce complex current responses under different cellular conditions that are expected to greatly affect the response of nociceptive neurons and other TRPV1-expressing cells
On Bismut Flat Manifolds
In this paper, we give a classification of all compact Hermitian manifolds
with flat Bismut connection. We show that the torsion tensor of such a manifold
must be parallel, thus the universal cover of such a manifold is a Lie group
equipped with a bi-invariant metric and a compatible left invariant complex
structure. In particular, isosceles Hopf surfaces are the only Bismut flat
compact non-K\"ahler surfaces, while central Calabi-Eckmann threefolds are the
only simply-connected compact Bismut flat threefolds.Comment: In this 3rd version, we add a lemma on Hermitian surfaces with flat
Riemannian connection. References are updated and typos correcte
Smooth quasi-developable surfaces bounded by smooth curves
Computing a quasi-developable strip surface bounded by design curves finds
wide industrial applications. Existing methods compute discrete surfaces
composed of developable lines connecting sampling points on input curves which
are not adequate for generating smooth quasi-developable surfaces. We propose
the first method which is capable of exploring the full solution space of
continuous input curves to compute a smooth quasi-developable ruled surface
with as large developability as possible. The resulting surface is exactly
bounded by the input smooth curves and is guaranteed to have no
self-intersections. The main contribution is a variational approach to compute
a continuous mapping of parameters of input curves by minimizing a function
evaluating surface developability. Moreover, we also present an algorithm to
represent a resulting surface as a B-spline surface when input curves are
B-spline curves.Comment: 18 page
The set of all orthogonal complex structures on the flat -tori
In \cite{BSV}, Borisov, Salamon and Viaclovsky constructed non-standard
orthogonal complex structures on flat tori for any . We will call these examples BSV-tori. In this note, we show that on a flat
-torus, all the orthogonal complex structures are either the complex tori or
the BSV-tori. This solves the classification problem for compact Hermitian
manifolds with flat Riemannian connection in the case of complex dimension
three.Comment: 14 page
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