Biharmonic maps on tangent and cotangent bundles
نویسندگان
چکیده
منابع مشابه
Tangent and Cotangent Bundles
of subsets of TM: Note that i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU = 1 (R) 2 : ii) If we de ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so (p; Xp) = ( (p); F ( Xp)); and 1 = ( 1 ; F 1 ): Now take 1 (U); 1 (V ) 2 and suppos...
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i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU = 1 (R) 2 . ii) If we de ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so (p; Xp) = ( (p); F ( Xp)); and 1 = ( 1 ; F 1 ). Now take 1 (U); 1 (V ) 2 and suppose (p; Xp) 2 1 (U)\ 1 (V ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2016
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2015.11.007