* Some Ukrainian team members leave Sochi due to upheaval
* Events in Ukraine leave mark on Russian Games
* Pussy Riot protest group release new video
* Top billing in sport is women's figure skating
By Mike Collett-White
SOCHI, Russia, Feb 20 (Reuters) - All eyes will be on the evening finale of the women's figure skating contest at the Winter Olympics on Thursday, but Russia's human rights record and its role in the crisis in neighbouring Ukraine succeeded in diverting the world's gaze.
The International Olympic Committee said some Ukrainian athletes had decided to leave Sochi for home, where at least 43 people have died in anti-government protests.
A team official said Alpine skier Bogdana Matsotska and her father, who is also her coach, had pulled out, although it was not immediately clear if others had joined them.
Turmoil at home has never been far from the minds of the Ukrainian team, and some athletes asked for permission on Wednesday to wear black arm bands while competing in order to honour those killed. Policemen were among the dead.
The IOC said it had not stopped athletes from doing so, but that the team had made the decision itself.
"I believe some of them have decided to return home and (Ukraine Olympic Committee president) Sergey Bubka has said he absolutely respects every individual's right to make their own decision," IOC spokesman Mark Adams told reporters.
Ukraine team officials and some athletes held a minute's silence in memory of the victims back home and black ribbons were attached to Ukraine flags hanging on the balconies of their building in the athletes' village.
Turmoil in Ukraine raises uncomfortable questions for Russia and its president, Vladimir Putin, who has been instrumental in shaping events in there.
Nationwide demonstrations erupted in November after Ukraine President Viktor Yanukovich bowed to Russian pressure and pulled out of a planned trade pact with the European Union, deciding instead to accept a Kremlin bailout for the indebted economy.
Putin will be desperate for the crisis not to overshadow the Games, which he has used to try to project a more modern, tolerant face of Russia through a well-organised Olympics and his own smiles, handshakes and hugs with athletes and officials.
Thrilling sporting action has generally pushed any criticism into the background, but it resurfaced this week with the detention in Sochi of members of protest group Pussy Riot, well known in the West for attacking Putin's human rights record.
They released a music video on Thursday criticising Russia's staging of the Winter Olympics that includes clips from an incident in Sochi when Cossacks beat members of the group with a whip as they tried to perform.
"The Olympics have created a space for the complete destruction of human rights in Russia," said Nadezhda Tolokonnikova, one of the group's most prominent members who has already been jailed for her protests.
"They have banned us from speaking. The rights of everyone are banned - political activists, LGBT (lesbian, gay, bisexual and transgender) activists and anyone who has an alternative opinion," she told reporters in Sochi.
KIM SEEKS TO RETAIN CROWN
In the sporting arena, six gold medals are decided on Thursday, led by the women's figure skating at the Iceberg Skating Palace in the Olympic Park.
Champion Kim Yuna of South Korea aims to become only the third woman to win back-to-back Olympic titles as the competition heads for a thrilling finale in the free dance.
Only a slender margin separates leader Kim from Russian Adelina Sotnikova and 2012 world champion Carolina Kostner of Italy, who is in third after the short programme.
Rising Russian star Julia Lipnitskaya failed to live up to a nation's expectations with a bad tumble that leaves the 15-year-old out of contention, and the home crowds were still smarting from Wednesday's men's ice hockey defeat by Finland.
There are also finals in women's ice hockey and curling, with Canada featuring in both.
The ice hockey final pits the United States against Canada, far and away the strongest teams in the sport. Canada have had the upper hand recently, beating the Americans 2-0 in the 2010 Vancouver final and 3-2 in the preliminary round in Sochi.
In curling, Canada's women face Sweden in another repeat of the 2010 final. The Swedes are seeking a third successive gold but face a tough challenge against a Canadian team who have marched to the final without suffering defeat.
Two medals are up for grabs in freestyle skiing at the Extreme Park up in the Caucasus Mountains above Sochi.
The first of those went to France's Jean-Frederic Chapuis in the men's ski cross, a thrilling spectacle of soaring jumps, tight, banked turns and painful tumbles.
American X-Games champion Maddie Bowman and Canadian runner-up Rosalind Groenewoud will start as favourites as women's ski halfpipe makes its Olympic debut.
Germany, backed by gold medallist Eric Frenzel, looks to be far too strong for opponents in Nordic Combined team event. (Reporting by the Reuters Olympic team in Sochi and Rosa Khutor; Editing by Peter Rutherford)