Laguna Beach Jeans Locally Symmetric Spaces of Com

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Locally Symmetric Spaces of Compact Hypersurfaces

Method [2b (+ whosoever) a <a) 』≥ 2nKS which is JlI,. The principal curvature, is. Cross-section rates at every point of the infimum. By the JlI, with parallel mean curvature vector and (1_) and (】 4), and noted that d ≤ K ≤ I, there. u ≥ a ns + H cylinder + ... + lj +2 Se, s + s2 a nHtrk0 Lemma 1, then a n + I, = k to IGr ≥ + Kat (i s) ≥ + {(a s) By Lemma 2, set A-it, a. fnHtrhf = nfHIltrl ≤ lHl √ million trit = n {Hl available by the elementary inequality (6) (7) (8) (9) (j0) (-n + I, ..., (12) (13) (】 (J5) (J6) (I7) 2 Yue Jin: a compact locally symmetric space smell hypersurface 33H & K. + - a I ≤ IHIΣ ten: + I, + llΣ wall, No. I) (18 ) from (15) ~ (18) had a ≥ a nS (state +2 n & S '+ s-+ A IH {/!'( 19) a direct calculation [8] 1 sound s a l + Jt2 ∞ by ( 19) and (20), use \u, ≥ s (2d-I) a (a 1) s] to use again.'s compact and Hopf principle, we prove Theorem 2.. lr.. reference to the text. offer., lHinc ~ S: Subnaarfifokkandtheo0ndfundamentalformLIrcNbtmJnMath.t984, 1156:19 d ~ 2032 Wuchuan Xi Ping Mu curvature of the sphere of childhood trip to the larvae _ 1 manifold of Hubei University, 1987,9 【1) 7 ~ l1_l: 3Cl ~ crs § s.DoCatmoMK ~ yashiS.Minima] Submanifold ~ of # . sp. herewithseeoadfundamen deleted formof ∞ n.statltlength.SSsc】 at ∞ PapetsSptin ~ \Add 05NolnizuK, SmithB.AFormulaofSimons | ypcand. nypersurfaeeswithcomtantmeancurvature, JDfffn, 1969,3:369 ~ 3776CleonBY, OkumuraScalarcurvature; Jneq ~ Oityands ~ ubmanifolds.Pr. c-fMaths0c,】 973,38: fi05 ~ 6087 Yue Jin, Wu Lu a normal bundle flat submanifolds Codimension reduction theorem. Hubei study of walking,】 991,13 (1】 {32 ~ 378 Yue Jin. with Parallel Mean Curvature Flow Tong's integral inequality. Wuhan University of Hydraulic and Electric, 199 ], 2d () {480 ~ .483 OntheCompactHypersurfacesinaLOcallySymmetricSImee ●. YucJing (DemrtmentofAppliedMathemi) AbstractnlispaperdealswiththbcompacthypersUrfaccs'ina-| ccal ~ symmctrieRiemannianmani-Lfold.Somcsufficientconditionsareobtained.underwhichthesquarclengthofthesecondfundan '~ n-talformoftheimmersedhypcrsdffaccsisconstant · Keywords when persurfaces; compactoperators; socondfundamentalformtlocallysymmefricspa ∞
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