Homogeneous Einstein -metrics on compact simple Lie groups and spheres
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- 作者：Zaili Yan<sup>asup><sup> ; sup><sup>yanzaili@nbu.edu.cn" class="auth_mail" title="E-mail the corresponding authorsup> ; Shaoqiang Deng<sup>bsup><sup> ; sup><sup>dengsq@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding authorsup>
- 关键词：53C21 ; 53C30 ; 53C60
- 刊名：Nonlinear Analysis
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：148
- 期：Complete
- 页码：147-160
- 全文大小：670 K
文摘
In this paper, we study homogeneous Einstein <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=561ee59c7a09ce05fabc91db207da099" title="Click to view the MathML source">(α,β)span><span class="mathContainer hidden"><span class="mathCode">span>span>span>-metrics on compact Lie groups and spheres. We first show that any left invariant Einstein <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=561ee59c7a09ce05fabc91db207da099" title="Click to view the MathML source">(α,β)span><span class="mathContainer hidden"><span class="mathCode">span>span>span>-metric on a connected compact simple Lie groups except <span id="mmlsi4" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si4.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=a52e27b0eb814cc3292942ddcb5ca75c">![]()
ss="imgLazyJSB inlineImage" height="13" width="35" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0362546X16302255-si4.gif">script>![]()
style="vertical-align:bottom" width="35" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0362546X16302255-si4.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span> with vanishing S-curvature must be a Randers metric. Secondly, we prove that any <span id="mmlsi5" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si5.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=8c5dcab0fccc57c3880422a206572b28">![]()
ss="imgLazyJSB inlineImage" height="13" width="57" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0362546X16302255-si5.gif">script>![]()
style="vertical-align:bottom" width="57" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0362546X16302255-si5.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>-invariant Einstein <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=561ee59c7a09ce05fabc91db207da099" title="Click to view the MathML source">(α,β)span><span class="mathContainer hidden"><span class="mathCode">span>span>span>-metric on <span id="mmlsi7" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si7.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=65d7e30d4c8c6d1539830f07993f323b" title="Click to view the MathML source">S<sup>4n+3sup>(n∈N<sup>+sup>)span><span class="mathContainer hidden"><span class="mathCode">span>span>span> with vanishing S-curvature is either a Randers metric, or <span id="mmlsi8" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si8.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=3c2cb8680abe935af97e37d3be05a739">![]()
ss="imgLazyJSB inlineImage" height="13" width="67" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0362546X16302255-si8.gif">script>![]()
style="vertical-align:bottom" width="67" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0362546X16302255-si8.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>-invariant. Finally, we give a complete description of <span id="mmlsi9" class="mathmlsrc">source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si9.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=f59eea0e254f465bd61eeaf569063b45">![]()
ss="imgLazyJSB inlineImage" height="13" width="60" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0362546X16302255-si9.gif">script>![]()
style="vertical-align:bottom" width="60" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0362546X16302255-si9.gif"> script><span class="mathContainer hidden"><span class="mathCode">span>span>span>-invariant Einstein Finsler metrics on <span id="mmlsi10" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302255&_mathId=si10.gif&_user=111111111&_pii=S0362546X16302255&_rdoc=1&_issn=0362546X&md5=ae54773e1f38f8c55a8c8341c0cc4436" title="Click to view the MathML source">S<sup>2n+1sup>(n≥2)span><span class="mathContainer hidden"><span class="mathCode">span>span>span>.