Some congruences for real algebraic curves on an ellipsoid

Some analogues of Gudkov–Rohlin, Kharlamov–Gudkov–Krakhnov, Kharlamov–Marin congruences are obtained in this paper for curves of odd degree on an ellipsoid. An analogue of Fiedler congruence is obtained for curves of even degree on an ellipsoid. In the appendix some generalizations of Rohlin and Kharlamov–Gudkov–Krakhnov congruences for curves oh surfaces are announced.