2017 # $f$-Biminimal immersions

**Abstract:** In the present paper, we define f -biminimal immersions. We consider f -biminimal curves in a Riemannian manifold and f -biminimal submanifolds of codimension 1 in a Riemannian manifold, and we give examples of fbiminimal surfaces. Finally, we consider f -biminimal Legendre curves in Sasakian space forms and give an example.

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“…An interpolating sesqui-harmonic map is biminimal if variations of (1.3) that are normal to the image ϕ(M) ⊂ N and δ 2 = 1, δ 1 > 0 [13]. For some recent study of biminimal immersions see [8], [13], [14] and [15].…”

confidence: 99%

“…An interpolating sesqui-harmonic map is biminimal if variations of (1.3) that are normal to the image ϕ(M) ⊂ N and δ 2 = 1, δ 1 > 0 [13]. For some recent study of biminimal immersions see [8], [13], [14] and [15].…”

confidence: 99%

“…An immersion ' is called to be f -biminimal [7] if it is critical points of the fbienergy functional E 2;f (') and f -energy functional E f (') for variations normal to the image '(M ) N; with …xed energy. Equivalently, there exists a constant 2 R such that ' is a critical point of the -f -bienergy functional…”

confidence: 99%

“…for some value of 2 R. It is called an immersion free f -biminimal if it is fbiminimal for = 0: If f is a constant, then the immersion is biminimal [7].…”

confidence: 99%

“…If the f -biharmonic map is neither harmonic nor biharmonic then we call it by proper f -biharmonic [21]. Biharmonic and f -biharmonic submanifolds have become popular in recent years (see [6], [13], [16], [20], [26], [27], [28]). In [3], Baikoussis and Blair gave a classification of 3-dimensional flat integral Cparallel submanifolds in the unit sphere S 7 (1) with the standard Sasakian structure.…”

confidence: 99%