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標題Title: A CONFORMAL INTEGRAL INVARIANT ON RIEMANNIAN FOLIATIONS
作者Authors: GUOFANG WANG AND YONGBING ZHANG
上傳單位Department: 電子工程系
上傳時間Date: 2012-12-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: manifold,conformal,foliation
摘要Abstract: Abstract. Let M be a closed manifold which admits a foliation structure F of codi-
mension q ≥ 2 and a bundle-like metric g0. Let [g0]B be the space of bundle-like metrics
which differ from g0 only along the horizontal directions by a multiple of a positive basic
function. Assume Y is a transverse conformal vector field and the mean curvature of the
T
leaves of (M, F, g0) vanishes. We show that the integral M Y (RgT )dμg is independent
of the choice of g ∈ [g0]B, where gT is the transverse metric induced by g and RT is
T
the transverse scalar curvature. Moreover if q ≥ 3, we have M Y (RgT )dμg = 0 for any
g ∈ [g0]B. However there exist codimension 2 minimal Riemannian foliations (M,F,g)
T
and transverse conformal vector fields Y such that M Y (RgT )dμg ≠ 0. Therefore, it
is a nontrivial obstruction for the transverse Yamabe problem on minimal Riemannian foliation of codimension 2.

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