Stability of stationary maps of a functional related to pullbacks of metrics

详细信息    查看全文

• 作者：Shigeo Kawai^a ; ^{kawais@cc.saga-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Nobumitsu Nakauchi^b ; ^{nakauchi@yamaguchi-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：58C43 ; 58E20 ; 58E99
• 刊名：Differential Geometry and its Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：44
• 期：Complete
• 页码：161-177
• 全文大小：361 K

文摘

Let an id="mmlsi1" class="mathmlsrc"><a title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si1.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=4d4c33f449b04ab76780e67317dfb423">ass="imgLazyJSB inlineImage" height="16" width="47" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0926224515001308-si1.gif">a>an class="mathContainer hidden">an class="mathCode">ath altimg="si1.gif" overflow="scroll">alse">(M,ace width="0.2em">ace>galse">)ath>an>an>an> and an id="mmlsi19" class="mathmlsrc"><a title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si19.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=25247647be693a03f83d3ff97c8047de">ass="imgLazyJSB inlineImage" height="16" width="45" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0926224515001308-si19.gif">a>an class="mathContainer hidden">an class="mathCode">ath altimg="si19.gif" overflow="scroll">alse">(N,ace width="0.2em">ace>halse">)ath>an>an>an> be Riemannian manifolds without boundary. We consider the functional for any smooth map an id="mmlsi4" class="mathmlsrc"><a title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si4.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=24012491d78b13c54fcab086c9d58690">ass="imgLazyJSB inlineImage" height="16" width="87" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0926224515001308-si4.gif">a>an class="mathContainer hidden">an class="mathCode">ath altimg="si4.gif" overflow="scroll">f:Mace width="0.2em">ace>alse">&rarr;ace width="0.2em">ace>Nath>an>an>an>, where an id="mmlsi5" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si5.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=8f88d1dc6c221b66726e13495a92f284" title="Click to view the MathML source">dv_gan>an class="mathContainer hidden">an class="mathCode">ath altimg="si5.gif" overflow="scroll">athvariant="normal">dvgath>an>an>an> is the volume form on an id="mmlsi1" class="mathmlsrc"><a title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si1.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=4d4c33f449b04ab76780e67317dfb423">ass="imgLazyJSB inlineImage" height="16" width="47" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0926224515001308-si1.gif">a>an class="mathContainer hidden">an class="mathCode">ath altimg="si1.gif" overflow="scroll">alse">(M,ace width="0.2em">ace>galse">)ath>an>an>an>, and an id="mmlsi6" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si6.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=795a0bc42f476689aad95c3f8dcc713c" title="Click to view the MathML source">‖f^⁎h‖an>an class="mathContainer hidden">an class="mathCode">ath altimg="si6.gif" overflow="scroll">alse">‖f⁎halse">‖ath>an>an>an> denotes the norm of the pullback an id="mmlsi7" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si7.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=5ffaa46a4c857ab194f640c8b881cba3" title="Click to view the MathML source">f^⁎han>an class="mathContainer hidden">an class="mathCode">ath altimg="si7.gif" overflow="scroll">f⁎hath>an>an>an> of the metric h by the map f  . We study stationary maps for the functional an id="mmlsi8" class="mathmlsrc">an class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0926224515001308&_mathId=si8.gif&_user=111111111&_pii=S0926224515001308&_rdoc=1&_issn=09262245&md5=5a8c739b1ce78f13cdbe2254cf8df9fe" title="Click to view the MathML source">Φ(f)an>an class="mathContainer hidden">an class="mathCode">ath altimg="si8.gif" overflow="scroll">athvariant="normal">Φalse">(false">)ath>an>an>an>, and show that stable stationary maps from or into minimal submanifolds in the unit spheres are rare if Ricci curvatures of submanifolds are large. Symmetric spaces of some type, which are minimally and isometrically immersed in the unit spheres, are treated in detail.