Adding constants or composing with a convex function would be OK as long as we have control on the derivative of this function (at infinity).

I put them on Arxiv first however peer reviewed and published papers count more than preprints.

Thank you. However the decoration in odd Khovanov homology seems to be to determine the signs and the authors say if one considers $\Z/2$ coefficients one does not need those decorations. Also the link surgeries spectral sequence (as described in Ozsvath and Szabo's branched double cover paper), doesn't seem to depend on the orientation of the link. (Although in Heegaard-Floer theory one assumes the manifold to be oriented and this together with the framing gives an orientation of the link.)

Thank you guys. I got the answer to my original question. However what if we mod out by the maximal torus? For example $U(n)/T^n$ is a flag variety and as the answe to to this Mathoverflow question mathoverflow.net/questions/7750/geodesics-on-a-grassmannian explains, the geodesics on it are given by $exp(tX)$ where $X$ lies in a complement of the Lie algebra of the maximal torus.

OK, thanks. But the round metric on $SU(2)\cong S^3$ has closed geodesics.