A woman found dead on Thursday in Brooklyn Park, a suburb of Minneapolis, was Ashley Hasti, according to a Facebook post from her sister, Alex.
Hasti was Sarkar's wife, officials in Hennepin County, Minnesota, said.
Hasti and Sarkar married June 14, 2011, Hennepin County Communications Officer Carolyn Marinan said. It was unclear whether they were married at the time of their deaths.
Police who searched Sarkar's Minnesota home found a note with an ominous title, Los Angeles police Chief Charlie Beck told reporters.
"Kill list," it said, spelling out the names of three people, according to Beck.
One of them was William S. Klug, the UCLA professor Sarkar killed with multiple gunshots, according to authorities.
A woman's name, apparently Hasti, also was on the list. She had been shot and had apparently been killed before the UCLA shooting, officials told reporters.
Hasti's body was found dead at 1:25 a.m. Thursday, according to the Hennepin County Medical Examiner's Office. She had multiple gunshot wounds.
Alex Hasti wrote of her sister: "Ashley Hasti ... was the smartest, coolest, and funniest person I knew. She could do anything she dreamed of whether it was studying abroad in four different countries, acting in school plays, trying stand up comedy and improv, and becoming a doctor. Unfortunately, she won't get to see that last dream come true as her life was cut short much too soon by her estranged husband."
The third person Sarkar intended to target was another professor at UCLA, Beck said. That faculty member was off-campus Wednesday and was unharmed, the police chief said.
Beck earlier told CNN affiliate KTLA-TV
that "a dispute over intellectual property" was tied to the UCLA shooting, which put the campus on lockdown for hours Wednesday.
"Everybody tries to look for a reason for this. Well, first of all, there is no good reason for this," Beck told the station. "This is a mental issue, mental derangement, but it was tied to a dispute over intellectual property."
Sarkar felt the professor he killed had released information "that harmed him," he told KTLA. "UCLA says this is absolutely not true. This is the workings of his imagination."
Police searching for vehicle
It had been several years since Sarkar was a student at UCLA. He graduated in 2013 with a Ph.D. in engineering.
At some point in the past few days, Beck said, Sarkar drove from his home in St. Paul, Minnesota, to Los Angeles, armed with two semiautomatic pistols and multiple rounds of ammunition.
He went to his former professor's fourth-floor office and shot him dead, then killed himself, Beck said.
Investigators who rushed to the scene found a note, according to the police chief.
"The note at UCLA said to ask for the finder to check on his cat in Minnesota. So we checked in (on) his cat in Minnesota at his residence. Actually we did a search warrant at his residence," Beck told KTLA.
That's where investigators found the kill list, Beck said.
Police are searching for the gray 2003 Nissan Sentra Sarkar drove from Minnesota to California, Beck said.
Inside, the police chief told KTLA, "there will be evidence that will help us unravel this."
Authorities don't have any evidence suggesting that Sarkar committed additional crimes on his way to California, Beck said. But that's something the police chief says they're investigating.
"Of course, that is one of the reasons we want to find the car," Beck said, "to see where that will lead us."
'Our entire UCLA family is mourning'
Sarkar was listed on a website for Klug's research group
at UCLA, and an online abstract
of his dissertation listed Klug as his adviser.
Klug's wife, Mary Elise Klug, issued a statement on Thursday thanking the public for its support and requesting privacy.
"During this extremely difficult time for our family, we are grateful for the tremendous outpouring of support. This is an indescribable loss. Bill was so much more than my soulmate. I will miss him every day for the rest of my life. Knowing that so many others share our family's sorrow has provided a measure of comfort," she said.
"That said, we are a very private family, and we need time to heal and recover from this senseless tragedy. At this time, we ask the media to please respect our family's privacy in and around our home, school and local community during the days and weeks ahead, especially for the sake of my children."
UCLA Chancellor Gene Block described the mechanical and aerospace engineering professor as "a respected, dedicated and caring faculty member" in a statement.
"Our entire UCLA family is mourning," he said.
Friends described the professor as an easygoing Little League coach. Lt. Gov. Gavin Newsom called him an "an empathetic, brilliant teacher."
A friend of Klug's fought back tears as he described the father of two to CNN affiliate KCBS-TV
"It's hard to even fathom," Lance Giroux said. "To have your son grow up without a dad, it's rough."
The professor was a proud coach of his young son's baseball team, friends told KCBS.
"(He was) always very positive. Kids loved working with him because he was such an easy coach to work with," Giroux said.
Klug's research group focused on theoretical and computation biomechanics, according to the university.
He received his undergraduate degree at Westmont College, then obtained a master's degree at UCLA and a Ph.D. from Caltech.
He joined UCLA's faculty in July 2003.
"Though the path to healing is long, we will make the journey together," Block said Thursday in his message to the campus. "Let us remember and be grateful for the wonderful gifts and talents professor Klug shared with us."
Los Angeles police said it got a call about the shooting around 10 a.m. PT Wednesday.
Officials put the campus on lockdown as authorities investigated. Throngs of police with long guns patrolled the streets of the campus of more than 40,000 students.
SWAT officers and dozens of squad cars filled the area as police tried to clear campus buildings floor by floor -- a task that CNN law enforcement analyst Tom Fuentes called "monumental."
UCLA's engineering building is in the middle of a densely populated part of Los Angeles.
The situation was contained shortly after noon, the police chief said. He said the shooting took place in a small office in the engineering building.
It was a jarring, tense time for the university's students. To protect themselves, some blocked doors with printers
, according to a picture on Twitter.
Freshman Teddi Mattox said she was in a cafeteria getting breakfast along with about 100 other students when the shooting occurred.
"We got the alert and a woman said, 'This is not a joke, everyone get to the back of the dining hall because we have to stay away from the windows,' " she said.
UCLA officials said they will review all campus safety procedures.
"We're pleased in the way notification went out, troubled by some reports of unlocked doors, but we want to review everything," said Scott Waugh, UCLA's executive vice chancellor and provost.
UCLA also extended counseling services over the next few days for students who may be in need, Waugh said.
Final exams are scheduled for next week, with graduation set for June 10.
The engineering school's senior class dinner was scheduled for Thursday night
Classes resumed for most of the university Thursday. At the engineering school, where the shooting occurred, classes will resume Monday, officials said.