Kovalevskaya's integrable case: generalizations and related new results

More than 11 decades have elapsed since S. V. Kovalevskaya discovered her famous case of integrability of the equations of motion of a heavy rigid body about a fixed point [1]. Nevertheless, the last 17 years have witnessed the emergence of some amazing and even unexpected results generalizing this case or valid under the same condition $A = B = 2C$. In this paper we give a summary of the known integrable cases of Kovalevskaya's type and point out some of their generalizations. A total of four general and five conditional integrable cases is listed. Of those, two general and three conditional cases are introduced for the first time.