Homogeneous Einstein -metrics on compact simple Lie groups and spheres

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• 作者：Zaili Yan^a ; ^{yanzaili@nbu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Shaoqiang Deng^b ; ^{dengsq@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 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 lsi1" class="mathmlsrc">lass="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)lass="mathContainer hidden">lass="mathCode">low="scroll">(α,β)-metrics on compact Lie groups and spheres. We first show that any left invariant Einstein lsi1" class="mathmlsrc">lass="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)lass="mathContainer hidden">lass="mathCode">low="scroll">(α,β)-metric on a connected compact simple Lie groups except lsi4" class="mathmlsrc">le="View the MathML 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">lass="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">lass="mathContainer hidden">lass="mathCode">low="scroll">le mathvariant="normal">SUle>(2) with vanishing S-curvature must be a Randers metric. Secondly, we prove that any lsi5" class="mathmlsrc">le="View the MathML 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">lass="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">lass="mathContainer hidden">lass="mathCode">low="scroll">le mathvariant="normal">Sple>(n+1)-invariant Einstein lsi1" class="mathmlsrc">lass="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)lass="mathContainer hidden">lass="mathCode">low="scroll">(α,β)-metric on lsi7" class="mathmlsrc">lass="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">S⁴ⁿ⁺³(n∈N⁺)lass="mathContainer hidden">lass="mathCode">low="scroll">S4n+3(n∈le-struck">N+) with vanishing S-curvature is either a Randers metric, or lsi8" class="mathmlsrc">le="View the MathML 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">lass="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">lass="mathContainer hidden">lass="mathCode">low="scroll">le mathvariant="normal">SUle>(2n+2)-invariant. Finally, we give a complete description of lsi9" class="mathmlsrc">le="View the MathML 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">lass="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">lass="mathContainer hidden">lass="mathCode">low="scroll">le mathvariant="normal">SUle>(n+1)-invariant Einstein Finsler metrics on lsi10" class="mathmlsrc">lass="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">S²ⁿ⁺¹(n≥2)lass="mathContainer hidden">lass="mathCode">low="scroll">S2n+1(n≥2).