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901.
902.
We show that if a closed manifold M admits an ℱ-structure (not necessarily polarized, possibly of rank zero) then its minimal entropy vanishes. In particular,
this is the case if M admits a non-trivial S
1-action. As a corollary we obtain that the simplicial volume of a manifold admitting an ℱ-structure is zero.?We also show
that if M admits an ℱ-structure then it collapses with curvature bounded from below. This in turn implies that M collapses with bounded scalar curvature or, equivalently, its Yamabe invariant is non-negative.?We show that ℱ-structures
of rank zero appear rather frequently: every compact complex elliptic surface admits one as well as any simply connected closed
5-manifold.?We use these results to study the minimal entropy problem. We show the following two theorems: suppose that M is a closed manifold obtained by taking connected sums of copies of S
4, ℂP
2,
2,S
2×S
2and the K3 surface. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
4,ℂP
2,S
2×S
2,ℂP
2#
2 or ℂP
2# ℂP
2. Finally, suppose that M is a closed simply connected 5-manifold. Then M has zero minimal entropy. Moreover, M admits a smooth Riemannian metric with zero topological entropy if and only if M is diffeomorphic to S
5,S
3×S
2, then on trivial S
3-bundle over S
2 or the Wu-manifold SU(3)/SO(3).
Oblatum 13-III-2002 & 12-VIII-2002?Published online: 8 November 2002
G.P. Paternain was partially supported by CIMAT, Guanajuato, México.?J. Petean is supported by grant 37558-E of CONACYT. 相似文献
903.
904.
Marco Andreatta 《manuscripta mathematica》2003,110(4):505-512
We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector
bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves
on projective manifolds.
Received: 16 May 2002 / Revised version: 18 November 2002 Published online: 3 March 2003
Mathematics Subject Classification (2000): 14E30, 14J40, 14J45 相似文献
905.
906.
Haihong Fang Binyuan Hu Lingshen Wang Rongli Lu Cui Yang 《Frontiers of Chemistry in China》2008,3(2):193-197
Nanometer MgO was prepared via a sol-gel auto-combustion technique using magnesium nitrate as raw material and citric acid
as chelating agent. IR spectra of the dried gel were used to investigate the structure of the precursors. By studying the
different TG curves of magnesium citrate gel prepared by different methods, we found that a combustion process occurred and
the nitrate ions acted as an oxidant in the combustion process. TEM photographs of synthesized powders from the sol-gel auto-combustion
showed that the crystallites were uniform in size. In addition, the XRD pattern of this sample showed that the particle size
was 8.9 nm. The BET curves, in turn, showed that the specific surface of the sample was 26.34 m2/g. The mechanism of the frothing process in restraining agglomeration is discussed.
__________
Translated from Journal of East China Normal University (Natural Science), 2007, (2): 52–57 [译自: 华东师范大学学报(自然科学版)] 相似文献
907.
Wenping Deng Gang Xu Lei Wan Anwen Liu Bo Gao Junhe Du Shuiming Hu Yang Chen 《Acta Physico》2008,24(8):1329-1334
Apparatus integrating a Fourier transform-infrared (FT-IR) spectrometer and a mid-infrared difference frequency generation (DFG) laser spectrometer was built for the study of the matrix isolation spectrum in solid molecular hydrogen. A 3-cm-long molecular hydrogen crystal was grown in a liquid-helium Dewar, and its infrared absorption spectrum in the 1-5 μm region was recorded to test the system. The W0(0) (ν=0←0, J=6←0) line around 2410 cm−1 of solid hydrogen was investigated with the DFG laser spectroscopy. High-resolution matrix isolation spectrum of CO2 co-deposited with hydrogen on a BaF2 cold plate at liquid-helium temperature was studied. 相似文献
908.
909.
910.