愛因斯坦卷積流形的不存在性問題-資料下載頁
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【正文】 xivo r g/ a bs/ 0805 . 3132 . [ 6 ] Chaki M C. O n qua si2Einstein manifolds [ J ] . Publ Mat h Debrecen ,2022 ,58 :6832691 . [ 7 ] De U C , De B K. O n qua si2Einstein ma nifolds [ J ] . Co m2 mun Ko rea n Mat h Soc ,2022 ,23 (3) :4132420 . [ 8 ] Ha milto n R S. The Ricci f lo w o n surf aces [ J ] . Co ntemp Mat h ,1988 ,71 :2372261 . [ 9 ] Hamilto n R S. The fo r matio n of singularitie s in t he Ricci f lo w [ C ]/ / Surveys in Diff erential Geo met r y , 2 . Co m2 bridge ,MA : Inter natio nal Pre ss ,1995 :72136 . [ 10 ] M ustaf a M T. A no n2exi stence re sult fo r co mp act Ei n2 stein wa rped p ro duct s [ J ] . J Phys A , 2022 , 38 : L 79122 L 793 . [ 11 ] Kim S. Wa rp ed p ro duct s a nd Einst ei n met ric s [J ] . J Phys ∫ B ( p , R) | Al n u | d x ≤ ∫ B ( p , R) | Al n u | d . A ,2022 ,39 :L 32922L 333 . 2 σ 9 接 下來利用 定 理 1 同樣 的 方法可以 證 明 u 是 正 的 常數(shù) ,所以 愛 因斯坦 卷 積流形是 平 凡 的 . [ 12 ] Qian Z. Estimate s fo r weighted vol umes and applicatio ns [J ] . Q uart J Mat h Oxfo r d Ser ,1997 ,190 :2352242 . Some Non2existence Problems f or Einstein Warped Products R U A N Qi2hua 3 , H U A N G Qi n (Depa rt ment of Mat hematic s , Putian U niver sit y , Putia n 351100 ,China) Abstract :In t hi s pap er ,we di scuss so me no n2exi stence p ro blems fo r Ricci f lat Einst ei n wa rp ed p ro duct s wit h a co mplete no nco mp act ba se . We p ro ve t hat if t he to tal scalar curvat ure of t he ba se i s no npo sitive o r t he warping f unctio n i s bo unded ,and t he vol ume gro wt h o n t he ba se sati sfie s so me co nditio ns ,t hen t here does no t exi st no n2t rivial Einst ei n wa rp ed p ro duct s. Key words :Einstein wa rped p ro duct s 。 warping f unctio n 。 vol ume gro wt h
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